Zobrazeno 1 - 10
of 118
pro vyhledávání: '"Adin, Ron M."'
We prove that, for any integer $k$, the $k$-th root enumerator in the classical Weyl group of type $D$ is a proper character. The proof uses higher Lie characters of type $B$.
Comment: 35 pages
Comment: 35 pages
Externí odkaz:
http://arxiv.org/abs/2312.08904
Autor:
Adin, Ron M., Roichman, Yuval
A new descent set statistic on involutions, defined geometrically via their interpretation as matchings, is introduced in this paper, and shown to be equi-distributed with the standard one. This concept is then applied to construct explicit cyclic de
Externí odkaz:
http://arxiv.org/abs/2210.14839
Autor:
Adin, Ron M., Roichman, Yuval
A character identity which relates irreducible character values of the hyperoctahedral group $B_n$ to those of the symmetric group $S_{2n}$ was recently proved by L\"ubeck and Prasad. Their proof is algebraic and involves Lie theory. We present a sho
Externí odkaz:
http://arxiv.org/abs/2107.11899
Several combinatorial actions of the affine Weyl group of type $\widetilde{C}_{n}$ on triangulations, trees, words and permutations are compared. Addressing a question of David Vogan, we show that, modulo a natural involution, these permutation repre
Externí odkaz:
http://arxiv.org/abs/2009.13880
A now-classical cyclic extension of the descent set of a permutation has been introduced by Klyachko and Cellini. Following a recent axiomatic approach to this notion, it is natural to ask which sets of permutations admit such an extension. The main
Externí odkaz:
http://arxiv.org/abs/1909.04460
The ring of cyclic quasi-symmetric functions and its non-Escher subring are introduced in this paper. A natural basis consists of fundamental cyclic quasi-symmetric functions; for the non-Escher subring they arise as toric $P$-partition enumerators,
Externí odkaz:
http://arxiv.org/abs/1811.05440
What is the minimal closed cone containing all $f$-vectors of cubical $d$-polytopes? We construct cubical polytopes showing that this cone, expressed in the cubical $g$-vector coordinates, contains the nonnegative $g$-orthant, thus verifying one dire
Externí odkaz:
http://arxiv.org/abs/1801.00163
A notion of cyclic descents on standard Young tableaux (SYT) of rectangular shape was introduced by Rhoades, and extended to certain skew shapes by the last two authors. The cyclic descent set restricts to the usual descent set when the largest value
Externí odkaz:
http://arxiv.org/abs/1801.00044
Publikováno v:
In Journal of Algebra 1 October 2022 607 Part A:5-33
Gessel conjectured that the two-sided Eulerian polynomial, recording the common distribution of the descent number of a permutation and that of its inverse, has non-negative integer coefficients when expanded in terms of the gamma basis. This conject
Externí odkaz:
http://arxiv.org/abs/1711.06511