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Permutation patterns, Stanley symmetric functions, and the Edelman-Greene correspondence

Authors
  • Billey, Sara
  • Pawlowski, Brendan
Publication Date
Jan 01, 2013
Source
HAL-UPMC
Keywords
Language
English
License
Unknown
External links

Abstract

Generalizing the notion of a vexillary permutation, we introduce a filtration of $S_{\infty}$ 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.

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