Bijections for rhombic alternative tableaux
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arXiv
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| Autores principales: | , , , |
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| Formato: | Preprint |
| Publicado: |
2026
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| Acceso en línea: | |
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| _version_ | 1866911512011997184 |
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| author | Corteel, Sylvie Kim, Jang Soo Mandelshtam, Olya Nadeau, Philippe |
| author_facet | Corteel, Sylvie Kim, Jang Soo Mandelshtam, Olya Nadeau, Philippe |
| contents | We generalize well-known bijections between alternative tableaux and permutations to bijections between rhombic alternative tableaux (RAT) and assemblées of permutations. We show how these various bijections are connected. As a consequence, we find a refined enumeration formula for RAT. One of our bijections carries many statistics from RAT to assemblées; notably, it sends the number of free cells to the number of crossings, which answers a question of Mandelshtam and Viennot. We also find an $r!$-to-$1$ map from marked Laguerre histories to assemblées, answering a question of Corteel and Nunge. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_12700 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Bijections for rhombic alternative tableaux Corteel, Sylvie Kim, Jang Soo Mandelshtam, Olya Nadeau, Philippe Combinatorics 05A15, 05A19 We generalize well-known bijections between alternative tableaux and permutations to bijections between rhombic alternative tableaux (RAT) and assemblées of permutations. We show how these various bijections are connected. As a consequence, we find a refined enumeration formula for RAT. One of our bijections carries many statistics from RAT to assemblées; notably, it sends the number of free cells to the number of crossings, which answers a question of Mandelshtam and Viennot. We also find an $r!$-to-$1$ map from marked Laguerre histories to assemblées, answering a question of Corteel and Nunge. |
| title | Bijections for rhombic alternative tableaux |
| topic | Combinatorics 05A15, 05A19 |
| url | https://arxiv.org/abs/2603.12700 |