An RSK correspondence for cylindric tableaux
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arXiv
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866908885008252928 |
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| author | Dobner, Alexander |
| author_facet | Dobner, Alexander |
| contents | This paper establishes an analogue of the Robinson--Schensted correspondence for cylindric tableaux. In particular, for any pair of positive integers $(d,L)$, we construct a bijection between permutations that avoid the patterns $d\cdots 1 (d+1)$ and $1\cdots (L+1)$ and pairs of $(d,L)$-cylindric standard Young tableaux with a common shape. This arises as a special case of a Knuth-type generalization involving cylindric semistandard tableaux and a further generalization involving oscillating tableaux. Using these results, we construct several other bijections and derive enumerative consequences involving cylindric tableaux and pattern-avoiding permutations. For example, we give an asymptotic for the number of permutations in $S_n$ that avoid the patterns $d\cdots 1 (d+1)$ and $1\cdots (L+1)$ as $n\to\infty$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_09119 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | An RSK correspondence for cylindric tableaux Dobner, Alexander Combinatorics 05A19 (Primary) 05A16, 05E10 (Secondary) This paper establishes an analogue of the Robinson--Schensted correspondence for cylindric tableaux. In particular, for any pair of positive integers $(d,L)$, we construct a bijection between permutations that avoid the patterns $d\cdots 1 (d+1)$ and $1\cdots (L+1)$ and pairs of $(d,L)$-cylindric standard Young tableaux with a common shape. This arises as a special case of a Knuth-type generalization involving cylindric semistandard tableaux and a further generalization involving oscillating tableaux. Using these results, we construct several other bijections and derive enumerative consequences involving cylindric tableaux and pattern-avoiding permutations. For example, we give an asymptotic for the number of permutations in $S_n$ that avoid the patterns $d\cdots 1 (d+1)$ and $1\cdots (L+1)$ as $n\to\infty$. |
| title | An RSK correspondence for cylindric tableaux |
| topic | Combinatorics 05A19 (Primary) 05A16, 05E10 (Secondary) |
| url | https://arxiv.org/abs/2603.09119 |