TY - JOUR

T1 - Permutation patterns, Stanley symmetric functions, and generalized Specht modules

AU - Billey, Sara

AU - Pawlowski, Brendan

PY - 2014/9

Y1 - 2014/9

N2 - Generalizing the notion of a vexillary permutation, we introduce a filtration of S ∞ 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.

AB - Generalizing the notion of a vexillary permutation, we introduce a filtration of S ∞ 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.

KW - Edelman-Greene correspondence

KW - Pattern avoidance

KW - Specht modules

KW - Stanley symmetric functions

UR - http://www.scopus.com/inward/record.url?scp=84901978596&partnerID=8YFLogxK

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U2 - 10.1016/j.jcta.2014.05.003

DO - 10.1016/j.jcta.2014.05.003

M3 - Article

AN - SCOPUS:84901978596

SN - 0097-3165

VL - 127

SP - 85

EP - 120

JO - Journal of Combinatorial Theory. Series A

JF - Journal of Combinatorial Theory. Series A

IS - 1

ER -