Permutation patterns, stanley symmetric functions, and the edelman-greene correspondence

Sara Billey, Brendan A Pawlowski

Research output: Contribution to journalConference articlepeer-review

Abstract

Generalizing the notion of a vexillary permutation, we introduce a filtration of S1 by the number of Edelman-Greene tableaux of a permutation, and show that each filtration level is characterized by avoiding a finite set of patterns. In doing so, we show that if w is a permutation containing v as a pattern, then there is an injection from the set of Edelman-Greene tableaux of v to the set of Edelman-Greene tableaux of w which respects inclusion of shapes. We also consider the set of permutations whose Edelman-Greene tableaux have distinct shapes, and show that it is closed under taking patterns.

Original languageEnglish (US)
Pages (from-to)205-216
Number of pages12
JournalDiscrete Mathematics and Theoretical Computer Science
StatePublished - Nov 18 2013
Event25th International Conference on Formal Power Series and Algebraic Combinatorics, FPSAC 2013 - Paris, France
Duration: Jun 24 2013Jun 28 2013

Keywords

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

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