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

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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https://hal.inria.fr/hal-01229705
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Sara Billey, Brendan Pawlowski. Permutation patterns, Stanley symmetric functions, and the Edelman-Greene correspondence. 25th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2013), 2013, Paris, France. pp.205-216. ⟨hal-01229705⟩

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