Cyclic Sieving of Increasing Tableaux
An $\textit{increasing tableau}$ is a semistandard tableau with strictly increasing rows and columns. It is well known that the Catalan numbers enumerate both rectangular standard Young tableaux of two rows and also Dyck paths. We generalize this to a bijection between rectangular 2-row increasing t...
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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 |
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| Online Access: | https://dmtcs.episciences.org/12815/pdf |
| _version_ | 1797270272829554688 |
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| author | Oliver Pechenik |
| author_facet | Oliver Pechenik |
| author_sort | Oliver Pechenik |
| collection | DOAJ |
| description | An $\textit{increasing tableau}$ is a semistandard tableau with strictly increasing rows and columns. It is well known that the Catalan numbers enumerate both rectangular standard Young tableaux of two rows and also Dyck paths. We generalize this to a bijection between rectangular 2-row increasing tableaux and small Schröder paths. Using the jeu de taquin for increasing tableaux of [Thomas–Yong '09], we then present a new instance of the cyclic sieving phenomenon of [Reiner–Stanton–White '04]. |
| first_indexed | 2024-04-25T02:01:38Z |
| format | Article |
| id | doaj.art-41662af97d2e4dddbfffff4a83198719 |
| institution | Directory Open Access Journal |
| issn | 1365-8050 |
| language | English |
| last_indexed | 2024-04-25T02:01:38Z |
| publishDate | 2013-01-01 |
| publisher | Discrete Mathematics & Theoretical Computer Science |
| record_format | Article |
| series | Discrete Mathematics & Theoretical Computer Science |
| spelling | doaj.art-41662af97d2e4dddbfffff4a831987192024-03-07T14:52:36ZengDiscrete Mathematics & Theoretical Computer ScienceDiscrete Mathematics & Theoretical Computer Science1365-80502013-01-01DMTCS Proceedings vol. AS,...Proceedings10.46298/dmtcs.1281512815Cyclic Sieving of Increasing TableauxOliver Pechenik0Department of Mathematics [Urbana]An $\textit{increasing tableau}$ is a semistandard tableau with strictly increasing rows and columns. It is well known that the Catalan numbers enumerate both rectangular standard Young tableaux of two rows and also Dyck paths. We generalize this to a bijection between rectangular 2-row increasing tableaux and small Schröder paths. Using the jeu de taquin for increasing tableaux of [Thomas–Yong '09], we then present a new instance of the cyclic sieving phenomenon of [Reiner–Stanton–White '04].https://dmtcs.episciences.org/12815/pdfincreasing tableauxcyclic sieving phenomenonk-promotionschröder pathschröder numbernoncrossing partition[info.info-dm]computer science [cs]/discrete mathematics [cs.dm] |
| spellingShingle | Oliver Pechenik Cyclic Sieving of Increasing Tableaux Discrete Mathematics & Theoretical Computer Science increasing tableaux cyclic sieving phenomenon k-promotion schröder path schröder number noncrossing partition [info.info-dm]computer science [cs]/discrete mathematics [cs.dm] |
| title | Cyclic Sieving of Increasing Tableaux |
| title_full | Cyclic Sieving of Increasing Tableaux |
| title_fullStr | Cyclic Sieving of Increasing Tableaux |
| title_full_unstemmed | Cyclic Sieving of Increasing Tableaux |
| title_short | Cyclic Sieving of Increasing Tableaux |
| title_sort | cyclic sieving of increasing tableaux |
| topic | increasing tableaux cyclic sieving phenomenon k-promotion schröder path schröder number noncrossing partition [info.info-dm]computer science [cs]/discrete mathematics [cs.dm] |
| url | https://dmtcs.episciences.org/12815/pdf |
| work_keys_str_mv | AT oliverpechenik cyclicsievingofincreasingtableaux |