On rotated Schur-positive sets

JOURNAL OF COMBINATORIAL THEORY SERIES A

卷:152

Article

Elizalde, Sergi¹  Roichman, Yuval² 

[1] Dartmouth Coll, Dept Math, 6188 Kemeny Hall, Hanover, NH 03755 USA

[2] Bar Ilan Univ, Dept Math, IL-52900 Ramat Gan, Israel

关键词: Schur-positivity;    Cyclic descent;    Standard Young tableau;    Horizontal rotation;    Cyclic action;   

DOI  :  10.1016/j.jcta.2017.06.002

来源: Elsevier

【 摘 要 】

The problem of finding Schur-positive sets of permutations, originally posed by Gessel and Reutenauer, has seen some recent developments. Schur-positive sets of pattern-avoiding permutations have been found by Sagan et al. and a general construction based on geometric operations on grid classes has been given by the authors. In this paper we prove that horizontal rotations of Schur-positive subsets of permutations are always Schur-positive. The proof applies a cyclic action on standard Young tableaux of certain skew shapes and a jeu-de-taquin type straightening algorithm. As a consequence of the proof we obtain a notion of cyclic descent set on these tableaux, which is rotated by the cyclic action on them. (C) 2017 Elsevier Inc. All rights reserved.

【 授权许可】

Free