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121 results on '"Graves, Christina"'

1. Pattern-restricted cyclic permutations with a pattern-restricted cycle form

Author

Archer, Kassie, Borsh, Ethan, Bridges, Jensen, Graves, Christina, and Jeske, Millie

Subjects
Mathematics - Combinatorics
Abstract

In this paper, we consider cyclic permutations that avoid the monotone decreasing permutation $k(k-1)\ldots 21$, whose cycle also demonstrates some pattern avoidance. If the cycle is written in standard form with 1 appearing at the beginning of the cycle and the standard form avoids a pattern of length 3, we find answers in terms of continued fraction generating functions. We also consider the case that every cyclic rotation of the cycle form of the permutation avoids a pattern of length 4 and enumerate two such cases.

Published
2024

2. Cyclic permutations avoiding patterns in both one-line and cycle forms

Author

Archer, Kassie, Borsh, Ethan, Bridges, Jensen, Graves, Christina, and Jeske, Millie

Subjects
Mathematics - Combinatorics, 05A05, 05A15, 05A10
Abstract

Let $\sigma$ and $\tau$ be patterns of length three; that is $\sigma, \tau \in \{123,132,213,231,312,321\}$. In this paper, we enumerate the set of cyclic permutations in $\mathcal{S}_n$ that avoid $\sigma$ in their one-line notation and another pattern $\tau$ in their cycle notation.

Published
2023

4. Pattern-restricted permutations composed of 3-cycles

Author

Archer, Kassie and Graves, Christina

Subjects
Mathematics - Combinatorics, 05A05, 05A19
Abstract

In this paper, we characterize and enumerate pattern-avoiding permutations composed of only 3-cycles. In particular, we answer the question for the six patterns of length 3. We find that the number of permutations composed of $n$ 3-cycles that avoid the pattern 231 (equivalently 312) is given by $3^{n-1}$, while the generating function for the number of those that avoid the pattern 132 (equivalently 213) is given by a formula involving the generating functions for the well-known Motzkin numbers and Catalan numbers. The number of permutations composed of $n$ 3-cycles that avoid the pattern 321 is characterized by a weighted sum involving statistics on Dyck paths of semilength~$n$.

Published
2021

5. Counting acyclic and strong digraphs by descents

Author

Archer, Kassie, Gessel, Ira M., Graves, Christina, and Liang, Xuming

Subjects
Mathematics - Combinatorics, 05C30 (primary), 05A15 (secondary)
Abstract

A descent of a labeled digraph is a directed edge (s, t) with s > t. We count strong tournaments, strong digraphs, and acyclic digraphs by descents and edges. To count strong tournaments we use Eulerian generating functions and to count strong and acyclic digraphs we use a new type of generating function that we call a graphic Eulerian generating function., Comment: 23 pages. Fixed typo

Published
2019
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10. Enumerating Acyclic Digraphs by Descents

Author

Archer, Kassie and Graves, Christina

Subjects
Mathematics - Combinatorics, 05C30, 05A19
Abstract

A descent of a labeled acyclic digraph is a directed edge $x\to y$ with $x>y$. In this paper, we find a recurrence for the number of labeled acyclic digraphs with a given number of descents.

Published
2017

17. More reliable graphs are not always stronger.

Author

Graves, Christina

Subjects
RANDOM graphs, GRAPH theory, SUBGRAPHS, POLYNOMIALS
Abstract

A graph G$$ G $$ is stronger than a graph H$$ H $$ if G$$ G $$ has at least as many connected spanning subgraphs of size k$$ k $$ as H$$ H $$ for any positive integer k$$ k $$. Counting the number of connected spanning subgraphs of fixed size allows us to compute the reliability of a graph. Formally, the reliability polynomial of a graph is the probability that the graph is connected when each edge is deleted independently with the same fixed probability. A graph G$$ G $$ is uniformly more reliable than H$$ H $$ if its reliability polynomial is greater than or equal to the reliability polynomial of H$$ H $$ for all probabilities. As a direct consequence of the definition, a sufficient condition for G$$ G $$ to be uniformly more reliable than H$$ H $$ is for G$$ G $$ to be stronger than H$$ H $$. In this paper, we show that the sufficient condition is not necessary by providing an example of two infinite families of graphs, Gk$$ {G}_k $$ and Hk$$ {H}_k $$, such that Gk$$ {G}_k $$ is uniformly more reliable than Hk$$ {H}_k $$ but is not stronger than Hk$$ {H}_k $$. [ABSTRACT FROM AUTHOR]

Published
2023
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18. Downstream mediators of the intratumoral interferon response suppress antitumor immunity, induce gemcitabine resistance and associate with poor survival in human pancreatic cancer

Author

Delitto, Daniel, Perez, Chelsey, Han, Song, Gonzalo, David H., Pham, Kien, Knowlton, Andrea E., Graves, Christina L., Behrns, Kevin E., Moldawer, Lyle L., Thomas, Ryan M., Liu, Chen, George, Jr., Thomas J., Trevino, Jose G., Wallet, Shannon M., and Hughes, Steven J.

Published
2015
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21. Tacit Knowledge

Author

Graves, Christina, Katz, Jerrold J., Nishiyama, Yuji, Soames, Scott, Stecker, Robert, and Tovey, Peter

Published
1973
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25. Lipid mediators and biomarkers associated with type 1 diabetes development

Author

Nelson, Alexander J., primary, Stephenson, Daniel J., additional, Bone, Robert N., additional, Cardona, Christopher L., additional, Park, Margaret A., additional, Tusing, Ying G., additional, Lei, Xiaoyong, additional, Kokotos, George, additional, Graves, Christina L., additional, Mathews, Clayton E., additional, Kramer, Joanna, additional, Hessner, Martin J., additional, Chalfant, Charles E., additional, and Ramanadham, Sasanka, additional

Published
2020
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31. Network reliability: Heading out on the highway.

Author

Brown, Jason I., Colbourn, Charles J., Cox, Danielle, Graves, Christina, and Mol, Lucas

Subjects
APPLIED mathematics, COMMUTATIVE algebra, ALGEBRAIC topology, PROBABILITY theory, GRAPH theory, COMBINATORICS
Abstract

A variety of probabilistic notions of network reliability of graphs and digraphs have been proposed and studied since the early 1950s. Although grounded in the engineering and logistics of network design and analysis, the research also spans pure and applied mathematics, with connections to areas as diverse as combinatorics and graph theory, combinatorial enumeration, optimization, probability theory, real and complex analysis, algebraic topology, commutative algebra, the design and analysis of algorithms, and computational complexity. In this paper we describe the landscape of various notions of network reliability, the roads well traveled, and some that appear likely to lead to meaningful and important journeys. [ABSTRACT FROM AUTHOR]

Published
2021
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32. Most reliable two‐terminal graphs with node failures.

Author

Brown, Isaac, Graves, Christina, Miller, Brendan, and Russell, Tyler

Subjects
UNDIRECTED graphs
Abstract

A two‐terminal graph is an undirected graph with two specified target vertices. If each nontarget vertex of a two‐terminal graph fails independently with the same fixed probability (and edges and target vertices are perfectly reliable), the two‐terminal node reliability is the probability that the target vertices are in the same connected component in the induced subgraph of all operational nodes. A two‐terminal graph is uniformly most reliable if its node reliability polynomial is greater than or equal to that of all other two‐terminal graphs with the same fixed number of vertices, n, and edges, m. In this paper, we show that there is always a uniformly most reliable two‐terminal graph. Furthermore, with the additional restriction that the distance between the target vertices is at least three, we completely classify which values of n and m produce a uniformly most reliable graph and which do not. [ABSTRACT FROM AUTHOR]

Published
2020
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37. Targeting resolution of neuroinflammation after ischemic stroke with a lipoxin A 4 analog: Protective mechanisms and long‐term effects on neurological recovery

Author

Hawkins, Kimberly E., primary, DeMars, Kelly M., additional, Alexander, Jon C., additional, Leon, Lauren G., additional, Pacheco, Sean C., additional, Graves, Christina, additional, Yang, Changjun, additional, McCrea, Austin O., additional, Frankowski, Jan C., additional, Garrett, Timothy J., additional, Febo, Marcelo, additional, and Candelario‐Jalil, Eduardo, additional

Published
2017
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39. Fullerene patches II

Author

Graver, Jack E., Graves, Christina M., and Graves, Stephen

Subjects
Physics::Atomic and Molecular Clusters
Abstract

In this paper, we show that fullerene patches with nice boundaries containing between 1 and 5 pentagons fall into several equivalence classes; furthermore, any two fullerene patches in the same class can be transformed into the same minimal configuration using combinatorial alterations.

Published
2014

40. Aging, inflammation, immunity and periodontal disease

Author

Ebersole, Jeffrey L., primary, Graves, Christina L., additional, Gonzalez, Octavio A., additional, Dawson, Dolph, additional, Morford, Lorri A., additional, Huja, Pinar Emecen, additional, Hartsfield, James K., additional, Huja, Sarandeep S., additional, Pandruvada, Subramanya, additional, and Wallet, Shannon M., additional

Published
2016
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41. Smallest graphs with given generalized quaternion automorphism group.

Author

Graves, Christina, Graves, Stephen J., and Lauderdale, L.‐K.

Subjects
*ISOMORPHISM (Mathematics), *QUATERNION functions, *AUTOMORPHISMS, *GEOMETRIC vertices, *PERMUTATION groups
Abstract

Abstract: For n ≥ 3, a smallest graph whose automorphism group is isomorphic to the generalized quaternion group is constructed. If n ≠ 3, then such a graph has 2 n + 1 vertices and 2 n + 2 edges. In the special case when n = 3, a smallest graph has 16 vertices but 44 edges. [ABSTRACT FROM AUTHOR]

Published
2018
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42. Human norovirus culture in B cells

Author

Jones, Melissa K, primary, Grau, Katrina R, additional, Costantini, Veronica, additional, Kolawole, Abimbola O, additional, de Graaf, Miranda, additional, Freiden, Pamela, additional, Graves, Christina L, additional, Koopmans, Marion, additional, Wallet, Shannon M, additional, Tibbetts, Scott A, additional, Schultz-Cherry, Stacey, additional, Wobus, Christiane E, additional, Vinjé, Jan, additional, and Karst, Stephanie M, additional

Published
2015
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