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arXiv · 2408.04086

The Latin Tableau Conjecture

Timothy Y. Chow·Mark G. Tiefenbruck
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Abstract

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 $μ$.

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Timothy Y. Chow, Mark G. Tiefenbruck. 2024-08-07. The Latin Tableau Conjecture. https://arxiv.org/abs/2408.04086

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