Permutation patterns, Stanley symmetric functions, and generalized Specht modules

JOURNAL OF COMBINATORIAL THEORY SERIES A

卷:127

Article

Billey, Sara¹  Pawlowski, Brendan¹ 

[1] Univ Washington, Dept Math, Seattle, WA 98195 USA

关键词: Edelman-Greene correspondence;    Stanley symmetric functions;    Specht modules;    Pattern avoidance;   

DOI  :  10.1016/j.jcta.2014.05.003

来源: Elsevier

【 摘 要 】

Generalizing the notion of a vexillary permutation, we introduce a filtration of S-infinity by the number of terms in the Stanley symmetric function, with the kth filtration level called the k-vexillary permutations. We show that for each k, the k-vexillary permutations are characterized by avoiding a finite set of patterns. A key step is the construction of a Specht series, in the sense of James and Peel, for the Specht module associated with the diagram of a permutation. As a corollary, we prove a conjecture of Liu on diagram varieties for certain classes of permutation diagrams. We apply similar techniques to characterize multiplicity-free Stanley symmetric functions, as well as permutations whose diagram is equivalent to a forest in the sense of Liu. (C) 2014 Elsevier Inc. All rights reserved.

【 授权许可】

Free