Search

Hovey and Palmieri [ The structure of the Bousfield lattice , Amer. Math. Soc., Providence, RI, 1999] proposed the retract conjecture on the Bousfield lattice of the stable homotopy category. The author, Shimomura and Tatehara [Publ. Res. Inst. Math. Sci. 50 (2014), pp. 497–513] defined the notion of monoidal posets as a generalization of the Bousfield lattice. In this paper, we prove that an analogue of the retract conjecture holds on a sublattice of monoidal posets. [ABSTRACT FROM AUTHOR]

Let G be a group and let k be a field. Kaplansky's direct finiteness conjecture states that every one-sided unit of the group ring k[G] must be a two-sided unit. In this paper, we establish a geometric direct finiteness theorem for endomorphisms of symbolic algebraic varieties. Whenever G is a sofic group or more generally a surjunctive group, our result implies a generalization of Kaplansky's direct finiteness conjecture for the near ring R(k,G) which is k[X_g\colon g \in G] as a group and which contains naturally k[G] as the subring of homogeneous polynomials of degree one. We also prove that Kaplansky's stable finiteness conjecture is a consequence of Gottschalk's Surjunctivity Conjecture. [ABSTRACT FROM AUTHOR]

Given a poset (P,≤), an antichain is a subset of pairwise incomparable elements of P. Let (P,w) be a graded, weighted poset. If the maximum weight of an antichain of P is equal to the weight of the largest rank of P, then P is said to be Sperner. In 1967, Rota conjectured that the poset of partitions, ordered by refinement of blocks, is Sperner; this conjecture was later disproved by Canfield. In this paper, we consider a generalization of Rota's conjecture and show that Sn, partially ordered by refinement of cycles, is strongly Sperner. [ABSTRACT FROM AUTHOR]

In 2000, Kadell gave an orthogonality conjecture for a symmetric function generalization of the Zeilberger-Bressoud q-Dyson theorem or the q-Dyson constant term identity. This conjecture was proved by Károlyi, Lascoux and Warnaar in 2015. In this paper, by slightly changing the variables of Kadell's conjecture, we obtain another symmetric function generalization of the q-Dyson constant term identity. This new generalized constant term admits a simple product-form expression. [ABSTRACT FROM AUTHOR]

As a natural generalization of the Euler-Mascheroni constant γ, Ihara introduced the Euler-Kronecker constant γKattached to any number field K. In this paper, we prove that a certain bound on γK in a tower of number fields K implies the generalized Brauer-Siegel conjecture for K as formulated by Tsfasman and Vladuţ. Moreover, we use known bounds on γK for cyclotomic fields to obtain a finer estimate for the number of zeros of the Dedekind zeta-function ζK(s) in the critical strip. [ABSTRACT FROM AUTHOR]