Permutation patterns, Stanley symmetric functions, and the Edelman-Greene correspondence
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 contai...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Discrete Mathematics & Theoretical Computer Science
2013-01-01
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| Series: | Discrete Mathematics & Theoretical Computer Science |
| Subjects: | |
| Online Access: | https://dmtcs.episciences.org/12805/pdf |
| _version_ | 1797270277704384512 |
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| author | Sara Billey Brendan Pawlowski |
| author_facet | Sara Billey Brendan Pawlowski |
| author_sort | Sara Billey |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-04-25T02:01:43Z |
| format | Article |
| id | doaj.art-53a9dfb8249e4b38853d2517bb12f9f0 |
| institution | Directory Open Access Journal |
| issn | 1365-8050 |
| language | English |
| last_indexed | 2024-04-25T02:01:43Z |
| publishDate | 2013-01-01 |
| publisher | Discrete Mathematics & Theoretical Computer Science |
| record_format | Article |
| series | Discrete Mathematics & Theoretical Computer Science |
| spelling | doaj.art-53a9dfb8249e4b38853d2517bb12f9f02024-03-07T14:52:36ZengDiscrete Mathematics & Theoretical Computer ScienceDiscrete Mathematics & Theoretical Computer Science1365-80502013-01-01DMTCS Proceedings vol. AS,...Proceedings10.46298/dmtcs.1280512805Permutation patterns, Stanley symmetric functions, and the Edelman-Greene correspondenceSara Billey0Brendan Pawlowski1Department of Mathematics [Seattle]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.https://dmtcs.episciences.org/12805/pdfedelman-greene correspondencestanley symmetric functionsspecht modulespattern avoidance[info.info-dm]computer science [cs]/discrete mathematics [cs.dm] |
| spellingShingle | Sara Billey Brendan Pawlowski Permutation patterns, Stanley symmetric functions, and the Edelman-Greene correspondence Discrete Mathematics & Theoretical Computer Science edelman-greene correspondence stanley symmetric functions specht modules pattern avoidance [info.info-dm]computer science [cs]/discrete mathematics [cs.dm] |
| title | Permutation patterns, Stanley symmetric functions, and the Edelman-Greene correspondence |
| title_full | Permutation patterns, Stanley symmetric functions, and the Edelman-Greene correspondence |
| title_fullStr | Permutation patterns, Stanley symmetric functions, and the Edelman-Greene correspondence |
| title_full_unstemmed | Permutation patterns, Stanley symmetric functions, and the Edelman-Greene correspondence |
| title_short | Permutation patterns, Stanley symmetric functions, and the Edelman-Greene correspondence |
| title_sort | permutation patterns stanley symmetric functions and the edelman greene correspondence |
| topic | edelman-greene correspondence stanley symmetric functions specht modules pattern avoidance [info.info-dm]computer science [cs]/discrete mathematics [cs.dm] |
| url | https://dmtcs.episciences.org/12805/pdf |
| work_keys_str_mv | AT sarabilley permutationpatternsstanleysymmetricfunctionsandtheedelmangreenecorrespondence AT brendanpawlowski permutationpatternsstanleysymmetricfunctionsandtheedelmangreenecorrespondence |