The CDE property for skew vexillary permutations

JOURNAL OF COMBINATORIAL THEORY SERIES A

卷:168

Article

Hopkins, Sam¹ 

[1] Univ Minnesota, Sch Math, Minneapolis, MN 55455 USA

关键词: Weak order;    Reduced word;    Coincidental down-degree expectations (CDE);    Vexillary permutation;    Semidistributive lattice;    Homomesy;    Rowmotion;    Grothendieck polynomial;   

DOI  :  10.1016/j.jcta.2019.06.005

来源: Elsevier

【 摘 要 】

We prove a conjecture of Reiner, Tenner, and Yong which says that the initial weak order intervals corresponding to certain vexillary permutations have the coincidental down-degree expectations (CDE) property. Actually our theorem applies more generally to certain skew vexillary permutations (a notion we introduce), and shows that these posets are in fact toggle CDE. As a corollary we obtain a homomesy result for rowmotion acting on semidistributive lattices in the sense of Barnard and of Thomas and Williams. (C) 2019 Elsevier Inc. All rights reserved.

【 授权许可】

Free