Identifying Orbit Lengths for Promotion
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866916813732839424 |
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| author | Catania, Elise Kendrick, Jack Russell, Heather M. Tymoczko, Julianna |
| author_facet | Catania, Elise Kendrick, Jack Russell, Heather M. Tymoczko, Julianna |
| contents | In this work we study Schützenberger's promotion operator on standard Young tableaux via a corresponding graphical construction known as $m-$diagrams. In particular, we prove that certain internal structures of SYT are preserved under promotion and correspond to distinct components of $m-$diagrams. By treating these structures as atomic parts of the $m-$diagram, we provide a simple algorithm for computing the promotion orbit length of rectangular SYT. We conclude the paper by applying our results to (column) semi-standard Young tableaux and prove a formula for the promotion orbit lengths of rectangular (column) SSYT. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_22306 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Identifying Orbit Lengths for Promotion Catania, Elise Kendrick, Jack Russell, Heather M. Tymoczko, Julianna Combinatorics Representation Theory In this work we study Schützenberger's promotion operator on standard Young tableaux via a corresponding graphical construction known as $m-$diagrams. In particular, we prove that certain internal structures of SYT are preserved under promotion and correspond to distinct components of $m-$diagrams. By treating these structures as atomic parts of the $m-$diagram, we provide a simple algorithm for computing the promotion orbit length of rectangular SYT. We conclude the paper by applying our results to (column) semi-standard Young tableaux and prove a formula for the promotion orbit lengths of rectangular (column) SSYT. |
| title | Identifying Orbit Lengths for Promotion |
| topic | Combinatorics Representation Theory |
| url | https://arxiv.org/abs/2506.22306 |