Geodesic
Permutation patterns, Stanley symmetric functions, and the Edelman-Greene correspondence
Discrete mathematics & theoretical computer science, DMTCS Proceedings vol. AS, 25th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2013), DMTCS Proceedings vol. AS, 25th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2013) (2013).

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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. 
@article{DMTCS_2013_special_264_a76,
     author = {Billey, Sara and Pawlowski, Brendan},
     title = {Permutation patterns, {Stanley} symmetric functions, and the {Edelman-Greene} correspondence},
     journal = {Discrete mathematics & theoretical computer science},
     publisher = {mathdoc},
     volume = {DMTCS Proceedings vol. AS, 25th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2013)},
     year = {2013},
     doi = {10.46298/dmtcs.12805},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.12805/}
}
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%J Discrete mathematics & theoretical computer science
%D 2013
%V DMTCS Proceedings vol. AS, 25th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2013)
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Billey, Sara; Pawlowski, Brendan. Permutation patterns, Stanley symmetric functions, and the Edelman-Greene correspondence. Discrete mathematics & theoretical computer science, DMTCS Proceedings vol. AS, 25th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2013), DMTCS Proceedings vol. AS, 25th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2013) (2013). doi : 10.46298/dmtcs.12805. http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.12805/

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