The Latin Tableau Conjecture
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866914905453494272 |
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| author | Chow, Timothy Y. Tiefenbruck, Mark G. |
| author_facet | Chow, Timothy Y. Tiefenbruck, Mark G. |
| contents | A Latin tableau of shape $λ$ and type $μ$ is a Young diagram of shape $λ$ in which each box contains a single positive integer, with no repeated integers in any row or column, and the $i$th most common integer appearing $μ_i$ times. Over twenty years ago, Chow et al., in their study of a generalization of Rota's basis conjecture that they called the wide partition conjecture, conjectured a necessary and sufficient condition for the existence of a Latin tableau of shape $λ$ and type $μ$. We report some computational evidence for this conjecture, and prove that the conjecture correctly characterizes, for any given $λ$, at least the first four parts of $μ$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_04086 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The Latin Tableau Conjecture Chow, Timothy Y. Tiefenbruck, Mark G. Combinatorics 05C15 A Latin tableau of shape $λ$ and type $μ$ is a Young diagram of shape $λ$ in which each box contains a single positive integer, with no repeated integers in any row or column, and the $i$th most common integer appearing $μ_i$ times. Over twenty years ago, Chow et al., in their study of a generalization of Rota's basis conjecture that they called the wide partition conjecture, conjectured a necessary and sufficient condition for the existence of a Latin tableau of shape $λ$ and type $μ$. We report some computational evidence for this conjecture, and prove that the conjecture correctly characterizes, for any given $λ$, at least the first four parts of $μ$. |
| title | The Latin Tableau Conjecture |
| topic | Combinatorics 05C15 |
| url | https://arxiv.org/abs/2408.04086 |