512 results on '"ASSOCIATION schemes (Combinatorics)"'
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2. Forum: Coding in Tongues: Developing Non-English Coding Schemes for Leadership Profiling.
- Author
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Brummer, Klaus, Young, Michael D, Özdamar, Özgur, Canbolat, Sercan, Thiers, Consuelo, Rabini, Christian, Dimmroth, Katharina, Hansel, Mischa, and Mehvar, Ameneh
- Subjects
- *
CODING theory , *INTERNATIONAL relations , *LEADERSHIP , *LANGUAGE & languages , *ASSOCIATION schemes (Combinatorics) - Abstract
Over the last twenty years since the introduction of automated coding schemes, research in foreign policy analysis (FPA) has made great advances. However, this automatization process is based on the analysis of verbal statements of leaders to create leadership profiles and has remained largely confined in terms of language. That is, the coding schemes can only parse English-language texts. This reduces both the quality and quantity of available data and limits the application of these leadership profiling techniques beyond the Anglosphere. Against this background, this forum offers five reports on the development of freely available coding schemes for either operational code analysis or leadership trait analysis for languages other than English (i.e. Turkish, Arabic, Spanish, German, and Persian). [ABSTRACT FROM AUTHOR]
- Published
- 2020
- Full Text
- View/download PDF
3. PATENT LAW DAMAGES: DEFINING AN INTELLIGIBLE STANDARD BETWEEN ATTORNEY'S FEES AND TREBLE DAMAGES.
- Author
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Tipton, Cole
- Subjects
ASSOCIATION schemes (Combinatorics) ,INDUSTRIAL laws & legislation ,MULTIPLE damages (Law) ,SANCTIONS (Social sciences) - Abstract
While the United States generally operates on a pay-yourown- way system that avoids punitive awards, current patent law standards seem to fly in the face of this general scheme. Following the ground-shaking cases of Octane Fitness and Halo, patent law now allows awards of both treble damages and attorney's fees after a mere showing of conduct akin to negligence. Defendants can be threatened with both of these crippling enhanced awards based on a totality of the circumstances showing of objective evidence. Moreover, awards of up to treble damages and attorney's fees are left entirely to the discretion of the trial judge--meaning that a successful appeal of a crippling double sanction is unlikely. Given patent law's departure from the traditional enhanced damages scheme and willingness to sanction conduct approaching mere negligence, a differentiation must be made between situations calling for treble damages and those calling for attorney's fees in order to avoid the draconian remedy of sanctioning the same conduct twice. [ABSTRACT FROM AUTHOR]
- Published
- 2020
4. On intriguing sets of the Penttila-Williford association scheme.
- Author
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Bamberg, John and Metsch, Klaus
- Subjects
- *
ASSOCIATION schemes (Combinatorics) , *CONSTRUCTION - Abstract
We investigate intriguing sets of an association scheme introduced by Penttila and Williford (2011) that was the basis for their construction of primitive cometric association schemes that are not P -polynomial nor the dual of a P -polynomial scheme. In particular, we give examples and characterisation results for the four types of intriguing sets that arise in this scheme. [ABSTRACT FROM AUTHOR]
- Published
- 2019
- Full Text
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5. Camina Triples and the Wedge Product of Association Schemes.
- Author
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Bagherian, Javad
- Subjects
- *
WEDGES , *ASSOCIATION schemes (Combinatorics) , *MANUFACTURED products , *CHARACTER - Abstract
In this paper, we first show that the group scheme of a Camina triple has the wedge product structure of association schemes. Then as a main result, we give a characterization of Camina triples in terms of their irreducible characters. [ABSTRACT FROM AUTHOR]
- Published
- 2019
- Full Text
- View/download PDF
6. Tight [formula omitted]-designs on one shell of Johnson association schemes.
- Author
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Bannai, Eiichi and Zhu, Yan
- Subjects
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ASSOCIATION schemes (Combinatorics) , *EVIDENCE , *ALGEBRA - Abstract
Each nontrivial shell (i.e., subconstituent) of the Johnson association scheme J (v , k) is known to be a commutative association scheme which is the product of two smaller Johnson association schemes. The concept of t -designs in one shell of J (v , k) was naturally defined and studied by Martin in the context of mixed t -designs. The purpose of this paper is to try to push this study a bit further. First we give a direct proof of the theorem that if (Y , w) is a relative t -design in J (v , k) on p shells then the part in each shell must be a weighted (t − p + 1) -design in the shell. In particular, it is a mixed (t − p + 1) -design in one shell if the weight function is constant on each shell. We also present another approach that makes use of the Terwilliger algebra, based on the work of Tanaka. This result is essentially proved by Martin in 1998, but the proof there contains a small gap which is repaired in this paper. We also study the existence problems of tight 2-, 3- and 4-designs on one shell of Johnson association scheme J (v , k) with small parameters, say v ≤ 1000 , thereby expanding the range of search in the original paper of Martin in 1998. [ABSTRACT FROM AUTHOR]
- Published
- 2019
- Full Text
- View/download PDF
7. Wedge-direct sums of table algebras and applications to association schemes, I.
- Author
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Xu, Bangteng
- Subjects
ALGEBRA ,ASSOCIATION schemes (Combinatorics) ,WEDGES ,WREATH products (Group theory) - Abstract
In the remarkable paper (Blau, J. Algebr. 396:220–271, 2013) on fusion rings, Blau introduced a very important operation on two table algebras (the Blau-construction). It is very difficult to describe the structure of table algebras obtained by recursively applying the Blau-construction. In this paper, we define the wedge-direct sum for a sequence of table algebras. Using the wedge-direct sum of a sequence of table algebras, we are able to not only give a clear description of the structure of table algebras obtained by recursively applying the Blau-construction but also obtain the characterization and classification of a class of p-table algebras. The structure of the Bose-Mesner algebras of the wreath products and wedge products of association schemes can also be clearly described in terms of the wedge-direct sum. As an application, we get some new and known results about the wreath products and wedge products of association schemes. [ABSTRACT FROM AUTHOR]
- Published
- 2019
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8. CONTINUOUS ASSOCIATION SCHEMES AND HYPERGROUPS.
- Author
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VOIT, MICHAEL
- Subjects
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ASSOCIATION schemes (Combinatorics) , *HYPERGROUPS , *SPHERICAL functions , *RANDOM walks , *COMBINATORIAL set theory - Abstract
Classical finite association schemes lead to finite-dimensional algebras which are generated by finitely many stochastic matrices. Moreover, there exist associated finite hypergroups. The notion of classical discrete association schemes can be easily extended to the possibly infinite case. Moreover, this notion can be relaxed slightly by using suitably deformed families of stochastic matrices by skipping the integrality conditions. This leads to a larger class of examples which are again associated with discrete hypergroups. In this paper we propose a topological generalization of association schemes by using a locally compact basis space $X$ and a family of Markov-kernels on $X$ indexed by some locally compact space $D$ where the supports of the associated probability measures satisfy some partition property. These objects, called continuous association schemes, will be related to hypergroup structures on $D$. We study some basic results for this notion and present several classes of examples. It turns out that, for a given commutative hypergroup, the existence of a related continuous association scheme implies that the hypergroup has many features of a double coset hypergroup. We, in particular, show that commutative hypergroups, which are associated with commutative continuous association schemes, carry dual positive product formulas for the characters. On the other hand, we prove some rigidity results in particular in the compact case which say that for given spaces $X,D$ there are only a few continuous association schemes. [ABSTRACT FROM AUTHOR]
- Published
- 2019
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9. On the association schemes with the thin radical series.
- Author
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Bagherian, Javad
- Subjects
- *
ASSOCIATION schemes (Combinatorics) , *WEDGES - Abstract
In this paper, we first show that the wedge product of a thin association scheme and a schurian association scheme is schurian. Then as an application of this result, we investigate the schurity problem for the association schemes having the thin radical series. We show that these association schemes are schurian under some conditions on the successive quotients of their thin radical series. [ABSTRACT FROM AUTHOR]
- Published
- 2019
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10. Association Schemes with at Most Two Nonlinear Irreducible Characters and Applications to Finite Groups.
- Author
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Bagherian, Javad
- Subjects
- *
FINITE groups , *ASSOCIATION schemes (Combinatorics) , *NONCOMMUTATIVE algebras , *CHARACTER , *MULTIPLICITY (Mathematics) - Abstract
An irreducible character χ of an association scheme is called nonlinear if the multiplicity of χ is greater than 1. The main result of this paper gives a characterization of commutative association schemes with at most two nonlinear irreducible characters. This yields a characterization of finite groups with at most two nonlinear irreducible characters. A class of noncommutative association schemes with at most two nonlinear irreducible character is also given. [ABSTRACT FROM AUTHOR]
- Published
- 2019
- Full Text
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11. Varietal Terwilliger algebras arising from wreath products of rank two association schemes.
- Author
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Xu, Bangteng
- Subjects
- *
WREATH products (Group theory) , *IDEMPOTENTS , *ASSOCIATION schemes (Combinatorics) , *LINEAR algebra - Abstract
Abstract As abstractions of Terwilliger algebras, generalized Terwilliger algebras and varietal Terwilliger algebras have been studied in [5,6,17]. In general, it is difficult to determine the structure of a varietal Terwilliger algebra. As proposed in the concluding remarks in [4] , in this paper we study the structures of those varietal Terwilliger algebras arising from the wreath products of rank two association schemes. In particular, we give the explicit formulas for their central primitive idempotents. Applications to Terwilliger algebras of association schemes are also discussed, and an affirmative answer to the Terwilliger conjecture mention in [4] is given. [ABSTRACT FROM AUTHOR]
- Published
- 2019
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12. Generalized wreath products of table algebras determined by their character tables and applications to association schemes.
- Author
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Chen, Gang and Xu, Bangteng
- Subjects
- *
WREATH products (Group theory) , *ASSOCIATION schemes (Combinatorics) , *COMPUTATIONAL mathematics , *FINITE groups , *COMPLEX numbers - Abstract
Abstract Structures of table algebras whose character tables have a zero submatrix were studied in Blau and Xu (2014) and Chen and Xu (2018). In this paper we continue the research in this direction, and investigate the conditions under which the character table with a zero submatrix yields a generalized wreath product of table algebras. Applications to association schemes are also discussed. [ABSTRACT FROM AUTHOR]
- Published
- 2019
- Full Text
- View/download PDF
13. On higher indicators of regular association schemes.
- Author
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Yoshikawa, Masayoshi
- Subjects
- *
ASSOCIATION schemes (Combinatorics) , *FINITE groups , *RATIONAL numbers , *INTEGERS , *PERIODIC functions - Abstract
In the present paper, we will define the higher Frobenius–Schur indicators and the higher indicators of association schemes as a generalization of those of finite groups. The higher indicators of any association scheme are always positive rational numbers. Especially, for any positive integer n , the n th indicator of any regular association scheme is the number of relations such that its strong girth divides n . Thus, all higher indicators of any regular association scheme are natural numbers, and the sequence of the indicators is periodic. We will show that the converses of these facts are also true for finite exponent association schemes. Finally, we introduce a family of infinite exponent association schemes all higher indicators of which are natural numbers and the sequence of the indicators of which is periodic. [ABSTRACT FROM AUTHOR]
- Published
- 2018
- Full Text
- View/download PDF
14. An efficient quantum teleportation of six-qubit state via an eight-qubit cluster state.
- Author
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Zhao, Nan, Li, Min, Chen, Nan, and Pei, Chang-xing
- Subjects
- *
QUANTUM teleportation , *CLUSTERING of particles , *QUANTUM entropy , *EVOLUTIONARY theories , *ASSOCIATION schemes (Combinatorics) - Abstract
We present a scheme for teleporting a certain class of six-particle state via an eight-particle cluster state as quantum channel. In our scheme, the sender merely needs to perform an eight-particle von-Neumann projective measurement, and the receiver gives a corresponding general evolution to restore the original state. Our scheme is a deterministic scheme. Compared with other schemes proposed before, our scheme possesses higher intrinsic efficiency. [ABSTRACT FROM AUTHOR]
- Published
- 2018
- Full Text
- View/download PDF
15. Autoequivalences of the category of schemes.
- Author
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Aizenbud, Avraham and Gal, Adam
- Subjects
- *
SCHEMES (Algebraic geometry) , *ASSOCIATION schemes (Combinatorics) , *MATHEMATICAL equivalence , *EQUIVALENCE relations (Set theory) , *MATHEMATICS theorems - Abstract
We prove that there is no non-trivial autoequvivalence of the category of schemes of finite type over Q . [ABSTRACT FROM AUTHOR]
- Published
- 2018
- Full Text
- View/download PDF
16. Non-commutative association schemes of rank 6 with affine subschemes.
- Author
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French, Christopher and Zieschang, Paul-Hermann
- Subjects
- *
ASSOCIATION schemes (Combinatorics) , *AUTOMORPHISM groups , *GRAPH theory , *INTEGERS , *VECTOR spaces - Abstract
When association schemes are viewed as a generalization of groups, it becomes natural to seek non-commutative examples. As with groups, non-commutative association schemes must have at least six elements, but unlike in group theory, there are numerous examples with exactly six elements. One method to try to classify such schemes is to attempt to construct extensions of schemes of rank 3, starting with those schemes of rank 3 which correspond to self-complementary strongly regular graphs with a vertex-transitive automorphism group. Recent work of Klin, Kriger, and Woldar provides new constructions for such graphs. In this paper, we investigate the possibility of constructing new non-commutative schemes with six elements from these graphs. [ABSTRACT FROM AUTHOR]
- Published
- 2018
- Full Text
- View/download PDF
17. An Assmus-Mattson theorem for codes over commutative association schemes.
- Author
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Morales, John Vincent S. and Tanaka, Hajime
- Subjects
ASSOCIATION schemes (Combinatorics) ,BLOCK codes ,LINEAR codes ,INTEGERS ,INTERPOLATION - Abstract
We prove an Assmus-Mattson-type theorem for block codes where the alphabet is the vertex set of a commutative association scheme (say, with
s classes). This in particular generalizes the Assmus-Mattson-type theorems for Z4-linear codes due to Tanabe (Des Codes Cryptogr 30:169-185, 2003 ) and Shin et al. (Des Codes Cryptogr 31:75-92,2004 ), as well as the original theorem by Assmus and Mattson (J Comb Theory 6:122-151,1969 ). The weights of a code ares -tuples of non-negative integers in this case, and the conditions in our theorem for obtainingt -designs from the code involve concepts from polynomial interpolation ins variables. The Terwilliger algebra is the main tool to establish our results. [ABSTRACT FROM AUTHOR]- Published
- 2018
- Full Text
- View/download PDF
18. m-Associate PBIB designs using Youden-m squares.
- Author
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Sharma, Kush and Garg, Davinder Kumar
- Subjects
- *
LEAST squares , *SET theory , *STATISTICAL association , *ASSOCIATION schemes (Combinatorics) , *COMBINATORICS - Abstract
In this paper, we have proposed a type of arrangement that we call Youden-m square and is similar to the usual Youden square but generates PBIB designs instead of BIB designs when its columns are taken as blocks. We have also discussed its construction methodologies, introduced two new m-associate class association schemes, and also constructed some series of Youden-m square type PBIB designs. [ABSTRACT FROM AUTHOR]
- Published
- 2018
- Full Text
- View/download PDF
19. Table algebras with central fusions.
- Author
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Xu, Bangteng
- Subjects
ALGEBRA ,FINITE groups ,ISOMORPHISM (Mathematics) ,ASSOCIATION schemes (Combinatorics) ,MULTIPLICITY (Mathematics) - Abstract
The character theory of table algebras is not as good as the character theory of finite groups. We introduce the notion of a table algebra with a central-fusion, in which the character theory has better properties. We study conditions under which a table algebra (
A ,B ) has a central-fusion, and its central-fusion is exactly isomorphic to the wreath product of the central-fusion of a quotient table algebra of (A ,B ) and another table algebra. As a consequence, we obtain a complete characterization of table algebras with exactly one irreducible character whose degree and multiplicity are not equal. Applications to association schemes are also discussed. [ABSTRACT FROM AUTHOR]- Published
- 2018
- Full Text
- View/download PDF
20. Association schemes and hypergroups.
- Author
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Jun, Jaiung
- Subjects
HYPERGROUPS ,ASSOCIATION schemes (Combinatorics) ,PROJECTIVE geometry ,ALGEBRA ,MATHEMATICS theorems - Abstract
In this paper, we investigate hypergroups which arise from association schemes in a canonical way; this class of hypergroups is called realizable. We first study basic algebraic properties of realizable hypergroups. Then we prove that two interesting classes of hypergroups (partition hypergroups and linearly ordered hypergroups) are realizable. Along the way, we prove that a certain class of projective geometries is equipped with a canonical association scheme structure which allows us to link three objects; association schemes, hypergroups, and projective geometries (see, Section 1.2 for details). [ABSTRACT FROM AUTHOR]
- Published
- 2018
- Full Text
- View/download PDF
21. New bounds for partial spreads of [formula omitted] and partial ovoids of the Ree–Tits octagon.
- Author
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Ihringer, Ferdinand, Sin, Peter, and Xiang, Qing
- Subjects
- *
HERMITIAN symmetric spaces , *MATHEMATICAL bounds , *PRIME numbers , *VOIDS (Crystallography) , *ASSOCIATION schemes (Combinatorics) , *MATHEMATICAL analysis - Abstract
Two results are obtained that give upper bounds on partial spreads and partial ovoids respectively. The first result is that the size of a partial spread of the Hermitian polar space H ( 3 , q 2 ) is at most ( ( 2 p 3 + p ) / 3 ) t + 1 , where q = p t , p is a prime. For fixed p this bound is in o ( q 3 ) , which is asymptotically better than the previous best known bound of ( q 3 + q + 2 ) / 2 . Similar bounds for partial spreads of H ( 2 d − 1 , q 2 ) , d even, are given. The second result is that the size of a partial ovoid of the Ree–Tits octagon O ( 2 t ) is at most 26 t + 1 . This bound, in particular, shows that the Ree–Tits octagon O ( 2 t ) does not have an ovoid. [ABSTRACT FROM AUTHOR]
- Published
- 2018
- Full Text
- View/download PDF
22. On the Construction of Combined Finite-Difference Schemes of High Accuracy.
- Author
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Kovyrkina, O. A. and Ostapenko, V. V.
- Subjects
- *
FINITE differences , *FINITE difference method , *ASSOCIATION schemes (Combinatorics) , *ORDERED groups , *MONOTONE operators - Abstract
A method is proposed for constructing combined shock-capturing finite-difference schemes that localize shock fronts with high accuracy and preserve the high order of convergence in all domains where the computed weak solution is smooth. A particular combined scheme is considered in which a nonmonotone compact scheme with a third-order weak approximation is used as a basis one, while the internal scheme is the second-order accurate (for smooth solutions) monotone CABARET. The advantages of the new scheme are demonstrated using test computations. [ABSTRACT FROM AUTHOR]
- Published
- 2018
- Full Text
- View/download PDF
23. Projection of Logistic Schemes in Intermodal Communications.
- Author
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ARBABEKOV, Muratbek I. and KUANYSHBAEV, Zhaken M.
- Subjects
ASSOCIATION schemes (Combinatorics) ,TARIFF ,TRANSPORTATION ,MONEY ,COMPUTER software - Abstract
This article reviews the question connected with determination of a carriage duty in the multimodal transportation system. In the following calculations is given the comparison between methodic of Rail - Tariff and methodic of United Transit Tariff (ETT). In terms of the research, through shoulder scheme of carriage duty based on the supranational currency EuroNur protected by certificate of the authorship is proposed. [ABSTRACT FROM AUTHOR]
- Published
- 2017
24. The motivic Steenrod algebra in positive characteristic.
- Author
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Hoyois, Marc, Kelly, Shane, and Arne Østvær, Paul
- Subjects
- *
STEENROD algebra , *MATHEMATICS , *COHOMOLOGY theory , *ASSOCIATION schemes (Combinatorics) , *INTEGRAL equations - Abstract
Let S be an essentially smooth scheme over a field and I ≠ char S a prime number. We show that the algebra of bistable operations in the mod I motivic cohomology of smooth S-schemes is generated by the motivic Steenrod operations. This was previously proved by Voevodsky for S a field of characteristic zero. We follow Voevodsky's proof but remove its dependence on characteristic zero by using etale cohomology instead of topological realization and by replacing resolution of singularities with a theorem of Gabber on alterations. [ABSTRACT FROM AUTHOR]
- Published
- 2017
- Full Text
- View/download PDF
25. On symmetric BIBDs with the same 3-concurrence.
- Author
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Chen, Zongchen and Zhao, Da
- Subjects
INCOMPLETE block designs ,HAMMING codes ,ASSOCIATION schemes (Combinatorics) ,BIPARTITE graphs ,MATHEMATICS theorems - Abstract
In a symmetric balanced incomplete block design (SBIBD), every pair of points appears $$\lambda $$ times among all blocks. In this paper, we study the 3-concurrence of an SBIBD, i.e., the number of times that each triple of points appears. We try to find two distinct SBIBDs whose 3-concurrences are exactly the same. Existence of such a pair would give a non-trivial tight relative 3-design on two shells in the binary Hamming association scheme H( n, 2). We prove that such pairs of designs do not exist when $$\lambda =1,2$$ or the block size is at least $$(\lambda -1)(\lambda ^2-2)+2$$ . We also give criteria to check the existence of such pairs when the designs are given. For $$\lambda =3$$ , our computational results show the non-existence of such pairs with only two cases left unknown: (45,12,3) and (71,15,3). [ABSTRACT FROM AUTHOR]
- Published
- 2017
- Full Text
- View/download PDF
26. Schur rings and association schemes whose thin residues are thin.
- Author
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Xu, Bangteng
- Subjects
- *
RING theory , *ASSOCIATION schemes (Combinatorics) , *AUTOMORPHISM groups , *MATHEMATICAL formulas , *GROUP theory - Abstract
The thin residue is an important concept in the theory of association schemes. Association schemes whose thin residues are thin have been studied in several papers. In this paper we construct a new class of association schemes whose thin residues are thin, and give a characterization of their automorphism groups. In particular, we give a formula for the order of the automorphism group, and a necessary and sufficient condition under which the association scheme is Schurian. Schur rings are used as a tool in our approach. [ABSTRACT FROM AUTHOR]
- Published
- 2017
- Full Text
- View/download PDF
27. Zeta functions for tensor products of locally coprime integral adjacency algebras of association schemes.
- Author
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Herman, Allen, Hirasaka, Mitsugu, and Oh, Semin
- Subjects
ZETA functions ,ALGEBRA ,REPRESENTATION theory ,ASSOCIATION schemes (Combinatorics) ,EULER products - Abstract
The zeta function of an integral lattice Λ is the generating function , whose coefficients count the number of left ideals of Λ of index n. We derive a formula for the zeta function of , where Λ
1 and Λ2 are ℤ-orders contained in finite-dimensional semisimple ℚ-algebras that satisfy a "locally coprime" condition. We apply the formula obtained above to ℤS⊗ℤT and obtain the zeta function of the adjacency algebra of the direct product of two finite association schemes (X,S) and (Y,T) in several cases where the ℤ-orders ℤS and ℤT are locally coprime and their zeta functions are known. [ABSTRACT FROM AUTHOR]- Published
- 2017
- Full Text
- View/download PDF
28. Model-Based Diversification for Sequential Exploratory Queries.
- Author
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Khan, Hina and Sharaf, Mohamed
- Subjects
ALGORITHMS ,QUERY (Information retrieval system) ,BIG data ,DATABASES ,ASSOCIATION schemes (Combinatorics) - Abstract
Today, data exploration platforms are widely used to assist users in locating interesting objects within large volumes of scientific and business data. In those platforms, users try to make sense of the underlying data space by iteratively posing numerous queries over large databases. While diversification of query results, like other data summarization techniques, provides users with quick insights into the huge query answer space, it adds additional complexity to an already computationally expensive data exploration task. To address this challenge, in this paper we propose a diversification scheme that targets the problem of efficiently diversifying the results of multiple queries within and across different data exploratory sessions. Our proposed scheme relies on a model-based diversification method and an ordered cache. In particular, we employ an adaptive regression model to estimate the diversity of a diverse subset. Such estimation of diversity value allows us to select diverse results without scanning all the query results. In order to further expedite the diversification process, we propose an order-based caching scheme to leverage the overlap between sequence of data exploration queries. Our extensive experimental evaluation on both synthetic and real data sets shows the significant benefits provided by our scheme as compared to the existing methods. [ABSTRACT FROM AUTHOR]
- Published
- 2017
- Full Text
- View/download PDF
29. Combinatorial extensions of Terwilliger algebras and wreath products of association schemes.
- Author
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Song, Sung Y., Xu, Bangteng, and Zhou, Shenglin
- Subjects
- *
COMBINATORIAL group theory , *WREATH products (Group theory) , *ASSOCIATION schemes (Combinatorics) , *ISOMORPHISM (Mathematics) , *COMMUTATIVE algebra - Abstract
We introduce the notion of the combinatorial extension of a Terwilliger algebra by a coherent algebra. By using this notion, we find a simple way to describe the Terwilliger algebras of certain coherent configurations as combinatorial extensions of simpler Terwilliger algebras. In particular, given an association scheme S and another association scheme R such that the Terwilliger algebra of R is isomorphic to a coherent algebra, we prove that the Terwilliger algebra of the wreath product S ≀ R is isomorphic to the combinatorial extension of the Terwilliger algebra of S by a coherent algebra. We also show that the Terwilliger algebra of the wreath product W of rank 2 association schemes can be expressed as the combinatorial extension of adjacency algebras of association schemes induced by the closed subsets of W . As a direct consequence, we obtain simple conceptual explanations and alternative proofs of many known results on the structures of Terwilliger algebras of wreath products of association schemes. [ABSTRACT FROM AUTHOR]
- Published
- 2017
- Full Text
- View/download PDF
30. Class dimension of association schemes in singular linear spaces.
- Author
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Guo, Haixia and Gao, You
- Subjects
- *
VECTOR spaces , *DIMENSIONS , *ASSOCIATION schemes (Combinatorics) , *MATHEMATICAL bounds , *SET theory , *INTEGERS - Abstract
A resolving set for an association scheme is a set of points such that, for all , the ordered list of relations uniquely determines , where denotes the relation containing the pair in . In this paper, we determine upper bounds on class dimension for a family of association schemes in singular linear spaces, and construct their resolving sets for a special case. [ABSTRACT FROM AUTHOR]
- Published
- 2017
- Full Text
- View/download PDF
31. A Family of Partial Geometric Designs from Three-Class Association Schemes.
- Author
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Nowak, Kathleen, Olmez, Oktay, and Song, Sung Y.
- Subjects
- *
ASSOCIATION schemes (Combinatorics) , *LINEAR codes , *ORTHOGONAL arrays , *REGULAR graphs , *SYMMETRIC functions - Abstract
In this paper, we show that partial geometric designs can be constructed from certain three-class association schemes and ternary linear codes with dual distance three. In particular, we obtain a family of partial geometric designs from the three-class association schemes introduced by Kageyama, Saha, and Das in their article ['Reduction of the number of associate classes of hypercubic association schemes,' Ann Inst Statist Math 30 (1978)]. We also give a list of directed strongly regular graphs arising from the partial geometric designs obtained in this paper. [ABSTRACT FROM AUTHOR]
- Published
- 2016
- Full Text
- View/download PDF
32. Secret image sharing with smaller shadow sizes for general access structures.
- Author
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Chen, Ying-Ru, Chen, Ling-Hwei, and Shyu, Shyong
- Subjects
ACCESS control ,COMPUTER file sharing ,ASSOCIATION schemes (Combinatorics) ,DATA security ,DECODING algorithms ,THRESHOLDING algorithms - Abstract
In the area of secret image sharing (SIS), most papers focused on the schemes for threshold or some special access structures. Regarding general access structures (GAS), few results have been found in the literature. Two SIS schemes for GAS were proposed in 2001 and 2010, both are based on qualified sets. However, one distorts the reconstructed secret image, and some extra information is needed in both schemes. Here, we propose three polynomial based SIS schemes for GAS. Considering either qualified or forbidden sets, these schemes can reconstruct the secret image perfectly without any extra information needed. Some proof and analysis on the shadow sizes of the three schemes are given to lead us to choose the one with the smallest size. In addition, we also give some comparisons with two existing schemes, and security issue is also addressed in conclusion. [ABSTRACT FROM AUTHOR]
- Published
- 2016
- Full Text
- View/download PDF
33. Cabinet approves Rs 1,650 crore for 75 lakh LPG connections under Ujjwala scheme.
- Subjects
LIQUEFIED petroleum gas ,ASSOCIATION schemes (Combinatorics) ,BENEFICIARIES - Abstract
The article highlights the government's approval to release Rs 1,650 crore to oil marketing companies for the provision of 75 lakh LPG connections under the Pradhan Mantri Ujjwala Yojana, and it will expand the total number of beneficiaries in the scheme to 10.35 crores.
- Published
- 2023
34. A Class of Imprimitive Association Schemes.
- Author
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Bagherian, Javad
- Subjects
SET theory ,ASSOCIATION schemes (Combinatorics) ,NONABELIAN groups ,MATHEMATICS theorems ,MATHEMATICAL proofs - Abstract
From Burnside'spαqβ-Theorem, it follows that any nonabelian group of orderpαqβ, wherepandqare primes, cannot be simple. As a main result of this article, we state and prove an analog of the mentioned theorem for commutative association schemes. [ABSTRACT FROM PUBLISHER]
- Published
- 2016
- Full Text
- View/download PDF
35. On the existence of self-complementary and non-self-complementary strongly regular graphs with Paley parameters.
- Author
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Klin, Mikhail, Kriger, Nimrod, and Woldar, Andrew
- Subjects
REGULAR graphs ,AFFINE geometry ,ASSOCIATION schemes (Combinatorics) ,PLANE geometry ,MATHEMATICAL analysis - Abstract
For p an odd prime, let $${{\mathcal A}_{p}}$$ be the complete classical affine association scheme whose associate classes correspond to parallel classes of lines in the classical affine plane AG(2, p). It is known that $${{\mathcal A}_{p}}$$ is an amorphic association scheme. We investigate rank 3 fusion schemes of $${{\mathcal A}_{p}}$$ whose basis graphs have the same parameters as the Paley graphs $${P(p^{2})}$$ . In contrast to the Paley graphs, the great majority of graphs we detect are non-self-complementary and non-Schurian. In particular, existence of non-self-complementary graphs with Paley parameters is established for $${p \ge 17}$$ , with an analogous existence result for non-Schurian such graphs when $${p \ge 11}$$ . We demonstrate that the number of self-complementary and non-self-complementary strongly regular graphs with Paley parameters grows rapidly as $${p \to \infty}$$ . [ABSTRACT FROM AUTHOR]
- Published
- 2016
- Full Text
- View/download PDF
36. Globally generated vector bundles on [formula omitted] with low first Chern classes.
- Author
-
Ballico, E., Huh, S., and Malaspina, F.
- Subjects
- *
VECTOR bundles , *CHERN classes , *ASSOCIATION schemes (Combinatorics) , *SMOOTHING (Numerical analysis) , *CURVES , *PROJECTIVE spaces - Abstract
We classify globally generated vector bundles on P 1 × P 1 × P 1 with small first Chern class, i.e. c 1 = ( a 1 , a 2 , a 3 ) , a i ≤ 2 . Our main method is to investigate the associated smooth curves to globally generated vector bundles via the Hartshorne–Serre correspondence. [ABSTRACT FROM AUTHOR]
- Published
- 2016
- Full Text
- View/download PDF
37. Association schemes in which the thin residue is an elementary abelian p-group of rank 2.
- Author
-
Hirasaka, Mitsugu and Kim, Kijung
- Subjects
- *
ASSOCIATION schemes (Combinatorics) , *ABELIAN groups , *EXISTENCE theorems , *ISOMORPHISM (Mathematics) , *VECTOR spaces , *MATHEMATICAL models - Abstract
In this article, we investigate the existence and schurity problem of association schemes whose thin residues are isomorphic to an elementary abelian p -group of rank 2. [ABSTRACT FROM AUTHOR]
- Published
- 2016
- Full Text
- View/download PDF
38. Terwilliger algebras of wreath products of association schemes.
- Author
-
Muzychuk, Mikhail and Xu, Bangteng
- Subjects
- *
ALGEBRA , *WREATH products (Group theory) , *GROUP theory , *ASSOCIATION schemes (Combinatorics) , *IDEMPOTENTS , *BOSE algebras - Abstract
The Terwilliger algebra of an association scheme of order n introduced in [13] is a subalgebra of the matrix algebra of all n × n matrices. Terwilliger algebras of wreath products of special association schemes are studied in several papers. In this paper we study the Terwilliger algebra of the wreath product T ≀ S of two arbitrary association schemes S and T . We will express the Terwilliger algebra of T ≀ S and its primitive central idempotents in terms of the Terwilliger algebras of S and T and their primitive central idempotents. The known results of Hanaki, Kim, etc. (cf. [7,10] ) are special cases of our results. [ABSTRACT FROM AUTHOR]
- Published
- 2016
- Full Text
- View/download PDF
39. Two classes of two-weight linear codes.
- Author
-
Heng, Ziling and Yue, Qin
- Subjects
- *
SET theory , *LINEAR codes , *ASSOCIATION schemes (Combinatorics) , *REGULAR graphs , *TERNARY codes , *BINARY codes , *HAMMING weight - Abstract
Two-weight linear codes have many wide applications in authentication codes, association schemes, strongly regular graphs, and secret sharing schemes. In this paper, we present two classes of two-weight binary or ternary linear codes. In some cases, they are optimal or almost optimal. They can also be used to construct secret sharing schemes. [ABSTRACT FROM AUTHOR]
- Published
- 2016
- Full Text
- View/download PDF
40. On association schemes of finite exponent.
- Author
-
Yoshikawa, Masayoshi
- Subjects
- *
ASSOCIATION schemes (Combinatorics) , *EXPONENTS , *GENERALIZATION , *FINITE groups , *GROUP theory , *SCHEMES (Algebraic geometry) - Abstract
The notion of an association scheme is a far reaching generalization of the notion of a group. During the past twenty years, many concepts and results in finite group theory have been generalized to finite scheme theory. In the present paper, we suggest two generalizations of the notion of the order of an element of a finite group by defining the girth and the strong girth of a relation of an association scheme on a finite set. We will show that the strong girth of a relation of a scheme is equal to its girth if its strong girth is finite. Similarly to the exponent of a finite group we define the exponent of an association scheme to be the least common multiple of the strong girths of its relations if all of them are finite. We will see that the exponent of a quotient scheme of a scheme S over a normal closed subset of S divides the exponent of S . An element s of an association scheme S will be called regular if s ∗ s s = { s } , and we will call an association scheme regular if each of its elements is regular. We will see that each regular association scheme is of finite exponent and that all association schemes of odd exponent are regular. Furthermore, we will show that any regular association scheme has a non-trivial thin radical. An application to commutative association schemes of finite order concludes our investigation. [ABSTRACT FROM AUTHOR]
- Published
- 2016
- Full Text
- View/download PDF
41. Isomorphism classes of association schemes induced by Hadamard matrices.
- Author
-
Hirasaka, Mitsugu, Kim, Kijung, and Yu, Hyonju
- Subjects
- *
ISOMORPHISM (Mathematics) , *SET theory , *ASSOCIATION schemes (Combinatorics) , *HADAMARD matrices , *CLUSTER algebras , *NUMBER theory - Abstract
Every Hadamard matrix H of order n > 1 induces a graph with 4 n vertices, called the Hadamard graph Γ ( H ) of H . Since Γ ( H ) is a distance-regular graph with diameter 4 , it induces a 4-class association scheme ( Ω , S ) of order 4 n . In this article we show a way to construct fission schemes of ( Ω , S ) under certain conditions, and for such a fission scheme we estimate the number of isomorphism classes with the same intersection numbers as the fission scheme. [ABSTRACT FROM AUTHOR]
- Published
- 2016
- Full Text
- View/download PDF
42. On numerical equivalence for algebraic cobordism.
- Author
-
Banerjee, Anandam and Park, Jinhyun
- Subjects
- *
MATHEMATICAL equivalence , *COBORDISM theory , *MODULES (Algebra) , *HOMOLOGY theory , *ASSOCIATION schemes (Combinatorics) , *COHOMOLOGY theory - Abstract
We define and study the notion of numerical equivalence on algebraic cobordism cycles. We prove that algebraic cobordism modulo numerical equivalence is a finitely generated module over the Lazard ring, and it reproduces the Chow group modulo numerical equivalence. We show this theory defines an oriented Borel–Moore homology theory on schemes and oriented cohomology theory on smooth varieties. We compare it with homological equivalence and smash-equivalence for cobordism cycles. For the former, we show that homological equivalence on algebraic cobordism is strictly finer than numerical equivalence, answering negatively the integral cobordism analogue of the standard conjecture ( D ). For the latter, using Kimura finiteness on cobordism motives, we partially resolve the cobordism analogue of a conjecture by Voevodsky on rational smash-equivalence and numerical equivalence. [ABSTRACT FROM AUTHOR]
- Published
- 2016
- Full Text
- View/download PDF
43. The scheme of liftings and applications.
- Author
-
Bertone, Cristina, Cioffi, Francesca, Guida, Margherita, and Roggero, Margherita
- Subjects
- *
MEASURE theory , *ASSOCIATION schemes (Combinatorics) , *LOCUS (Mathematics) , *IDEALS (Algebra) , *POLYNOMIAL rings , *GROBNER bases - Abstract
We study the locus of the liftings of a homogeneous ideal H in a polynomial ring over any field. We prove that this locus can be endowed with a structure of scheme L H by applying the constructive methods of Gröbner bases, for any given term order. Indeed, this structure does not depend on the term order, since it can be defined as the scheme representing the functor of liftings of H . We also provide an explicit isomorphism between the schemes corresponding to two different term orders. Our approach allows to embed L H in a Hilbert scheme as a locally closed subscheme, and, over an infinite field, leads to finding interesting topological properties, as for instance that L H is connected and that its locus of radical liftings is open. Moreover, we show that every ideal defining an arithmetically Cohen–Macaulay scheme of codimension two has a radical lifting, giving in particular an answer to an open question posed by L.G. Roberts in 1989. [ABSTRACT FROM AUTHOR]
- Published
- 2016
- Full Text
- View/download PDF
44. Association schemes based on the subspaces of type [formula omitted] in singular symplectic space over finite fields.
- Author
-
Wang, Rui and Gao, You
- Subjects
- *
ASSOCIATION schemes (Combinatorics) , *SUBSPACES (Mathematics) , *SYMPLECTIC spaces , *FINITE fields , *MATHEMATICAL analysis - Abstract
In this paper, we provide a construction of association scheme based on the subspaces of type ( 2 , 1 , 0 ) in singular symplectic space over finite fields. Moreover, all parameters of the association scheme are computed. [ABSTRACT FROM AUTHOR]
- Published
- 2015
- Full Text
- View/download PDF
45. A Schur–Zassenhaus Theorem for association schemes.
- Author
-
French, Christopher and Zieschang, Paul-Hermann
- Subjects
- *
ASSOCIATION schemes (Combinatorics) , *FINITE groups , *GROUP theory , *SUBGROUP growth , *GENERALIZATION - Abstract
Conditions are given under which a normal closed subset of an association scheme of finite order possesses a complement. Our attempts are in the spirit of the Schur–Zassenhaus Theorem on finite groups and partially generalize that theorem. [ABSTRACT FROM AUTHOR]
- Published
- 2015
- Full Text
- View/download PDF
46. Perfect state transfer on distance-regular graphs and association schemes.
- Author
-
Coutinho, G., Godsil, C., Guo, K., and Vanhove, F.
- Subjects
- *
REGULAR graphs , *ASSOCIATION schemes (Combinatorics) , *GRAPH theory , *CONTINUOUS time systems , *MATHEMATICAL analysis - Abstract
We consider the representation of a continuous-time quantum walk in a graph X by the matrix exp ( − i t A ( X ) ) . We provide necessary and sufficient criteria for distance-regular graphs and, more generally, for graphs in association schemes to have perfect state transfer. Using these conditions, we provide several new examples of perfect state transfer in simple graphs. [ABSTRACT FROM AUTHOR]
- Published
- 2015
- Full Text
- View/download PDF
47. Self-dual codes from 3-class association schemes.
- Author
-
Bilal, M., Borges, J., Dougherty, S., and Fernández-Córdoba, C.
- Subjects
- *
ASSOCIATION schemes (Combinatorics) , *CODING theory , *MATHEMATICAL symmetry , *NUMBER theory , *COMBINATORICS - Abstract
3-Class association schemes are used to construct binary self-dual codes. We use the pure and bordered construction to get self-dual codes starting from the adjacency matrices of symmetric and non-symmetric 3-class association schemes. In some specific cases, we also study constructions of self-dual codes over $${\mathbb {Z}}_k$$ . For symmetric 3-class association schemes, we focus on the rectangular scheme and association schemes derived from symmetric designs. [ABSTRACT FROM AUTHOR]
- Published
- 2015
- Full Text
- View/download PDF
48. Several Anzahl theorems of alternate matrices over Galois rings.
- Author
-
Guo, Jun and Li, Fenggao
- Subjects
- *
GALOIS rings , *CARDINAL numbers , *LINEAR algebra , *ASSOCIATION schemes (Combinatorics) , *ORBIT method - Abstract
Let R denote the Galois ring of characteristic p s and cardinality p s h . In this paper, we determine the Smith normal forms of alternate matrices over R , compute the number of the orbits of n × n alternate matrices under the group GL n ( R ) and the length of each orbit. Moreover, we discuss their applications to authentication codes and association schemes. [ABSTRACT FROM AUTHOR]
- Published
- 2015
- Full Text
- View/download PDF
49. A new family of relative hemisystems on the Hermitian surface.
- Author
-
Cossidente, Antonio
- Subjects
HERMITIAN forms ,FINITE generalized quadrangles ,ASSOCIATION schemes (Combinatorics) ,INCIDENCE functions ,AUTOMORPHISM groups - Abstract
A new family of relative hemisystems on the generalized quadrangle H(3,q
2 ) admitting a group of order q2 (q + 1) as automorphism group, is constructed. As a by product a new infinite family of hyperovals of H(3,q2 ) is presented. [ABSTRACT FROM AUTHOR]- Published
- 2015
- Full Text
- View/download PDF
50. End-to-end mobility support in content centric networks.
- Author
-
Kim, Do‐hyung, Kim, Jong‐hwan, Kim, Yu‐sung, Yoon, Hyun‐soo, and Yeom, Ikjun
- Subjects
- *
END-to-end delay , *INTERNET protocols , *COMPUTER architecture , *ASSOCIATION schemes (Combinatorics) , *COMPUTER networks , *INFORMATION services - Abstract
Content-centric networking (CCN) has been recently proposed as an alternative to traditional IP-based networking. In CCN, content is accessed by content name instead of a host identifier (locational identifier). This new type of access methodology rapidly and efficiently disseminates content in combination with the in-network caching mechanism. For practical use of CCN, many network properties studied in IP-based networking are being revisited, and new types of CCN architecture components are being designed. Although mobility is an essential aspect of the future networking system, it has not been sufficiently studied. We therefore address fundamental mobility issues, such as seamless handover, optimal access point selection, network mobility, and handling of persistent interests. In addition, for each issue, we propose practical solutions that efficiently align to a CCN environment. To ensure seamless handoff, we propose various handoff schemes and compare their performance in terms of handoff latency using packet-level simulation. Because our proposed schemes are consistent with the characteristics and rules of CCN, we believe that they can easily be integrated as a part of CCN. Copyright © 2014 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]
- Published
- 2015
- Full Text
- View/download PDF
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