A generalization of RSK to $d$-complete posets
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866909747539607552 |
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| author | Nguyen, Son Vulakh, Joseph Woodruff, Dora |
| author_facet | Nguyen, Son Vulakh, Joseph Woodruff, Dora |
| contents | The hook length formula for $d$-complete posets expresses the number of linear extensions of a $d$-complete poset $P$ in terms of hooks of $P$. It generalizes the usual hook length formula for standard Young tableaux, as well as hook length formulas for shifted Young tableaux and trees. We give a new proof of the hook length formula for $d$-complete posets which is elementary and purely combinatorial. Our approach is to define a generalization of the Robinson-Schensted-Knuth bijection for $d$-complete posets, which may be of independent interest. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_13988 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A generalization of RSK to $d$-complete posets Nguyen, Son Vulakh, Joseph Woodruff, Dora Combinatorics 05A19 The hook length formula for $d$-complete posets expresses the number of linear extensions of a $d$-complete poset $P$ in terms of hooks of $P$. It generalizes the usual hook length formula for standard Young tableaux, as well as hook length formulas for shifted Young tableaux and trees. We give a new proof of the hook length formula for $d$-complete posets which is elementary and purely combinatorial. Our approach is to define a generalization of the Robinson-Schensted-Knuth bijection for $d$-complete posets, which may be of independent interest. |
| title | A generalization of RSK to $d$-complete posets |
| topic | Combinatorics 05A19 |
| url | https://arxiv.org/abs/2508.13988 |