Sara Billey ; Brendan Pawlowski - Permutation patterns, Stanley symmetric functions, and the Edelman-Greene correspondence

dmtcs:12805 - Discrete Mathematics & Theoretical Computer Science, January 1, 2013, DMTCS Proceedings vol. AS, 25th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2013) - https://doi.org/10.46298/dmtcs.12805
Permutation patterns, Stanley symmetric functions, and the Edelman-Greene correspondenceArticle

Authors: Sara Billey 1; Brendan Pawlowski 1

  • 1 Department of Mathematics [Seattle]

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.


Volume: DMTCS Proceedings vol. AS, 25th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2013)
Section: Proceedings
Published on: January 1, 2013
Imported on: November 21, 2016
Keywords: Edelman-Greene correspondence,Stanley symmetric functions,Specht modules,pattern avoidance,[INFO.INFO-DM]Computer Science [cs]/Discrete Mathematics [cs.DM]

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