Permutation patterns, Stanley symmetric functions, and generalized Specht modules

Sara Billey, Brendan Pawlowski

Research output: Contribution to journalArticlepeer-review

4 Scopus citations

Abstract

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.

Original languageEnglish (US)
Pages (from-to)85-120
Number of pages36
JournalJournal of Combinatorial Theory. Series A
Volume127
Issue number1
DOIs
StatePublished - Sep 2014

Keywords

  • Edelman-Greene correspondence
  • Pattern avoidance
  • Specht modules
  • Stanley symmetric functions

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