Bender-Knuth involutions on linear extensions of posets
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arXiv
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| Hauptverfasser: | , , , , , , |
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| Format: | Preprint |
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2023
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| _version_ | 1866917621253799936 |
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| author | Chiang, Judy Hsin-Hui Hoang, Anh Trong Nam Kendall, Matthew Lynch, Ryan Nguyen, Son Przybocki, Benjamin Xia, Janabel |
| author_facet | Chiang, Judy Hsin-Hui Hoang, Anh Trong Nam Kendall, Matthew Lynch, Ryan Nguyen, Son Przybocki, Benjamin Xia, Janabel |
| contents | We study the permutation group $\mathcal{BK}_P$ generated by Bender-Knuth moves on linear extensions of a poset $P$, an analog of the Berenstein-Kirillov group on column-strict tableaux. We explore the group relations, with an emphasis on identifying posets $P$ for which the cactus relations hold in $\mathcal{BK}_P$. We also examine $\mathcal{BK}_P$ as a subgroup of the symmetric group $\mathfrak{S}_{\mathcal{L}(P)}$ on the set of linear extensions of $P$ with the focus on analyzing posets $P$ for which $\mathcal{BK}_P = \mathfrak{S}_{\mathcal{L}(P)}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2302_12425 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Bender-Knuth involutions on linear extensions of posets Chiang, Judy Hsin-Hui Hoang, Anh Trong Nam Kendall, Matthew Lynch, Ryan Nguyen, Son Przybocki, Benjamin Xia, Janabel Combinatorics Representation Theory 06A07, 20B25 We study the permutation group $\mathcal{BK}_P$ generated by Bender-Knuth moves on linear extensions of a poset $P$, an analog of the Berenstein-Kirillov group on column-strict tableaux. We explore the group relations, with an emphasis on identifying posets $P$ for which the cactus relations hold in $\mathcal{BK}_P$. We also examine $\mathcal{BK}_P$ as a subgroup of the symmetric group $\mathfrak{S}_{\mathcal{L}(P)}$ on the set of linear extensions of $P$ with the focus on analyzing posets $P$ for which $\mathcal{BK}_P = \mathfrak{S}_{\mathcal{L}(P)}$. |
| title | Bender-Knuth involutions on linear extensions of posets |
| topic | Combinatorics Representation Theory 06A07, 20B25 |
| url | https://arxiv.org/abs/2302.12425 |