A Latin tableau of shape $\lambda$ and type $\mu$ is a Young diagram of shape $\lambda$ 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 $\mu_i$ 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 $\lambda$ and type $\mu$. We report some computational evidence for this conjecture, and prove that the conjecture correctly characterizes, for any given $\lambda$, at least the first four parts of $\mu$.
@article{10_37236_13248,
author = {Timothy Y. Chow and Mark G. Tiefenbruck},
title = {The {Latin} tableau conjecture},
journal = {The electronic journal of combinatorics},
year = {2025},
volume = {32},
number = {2},
doi = {10.37236/13248},
zbl = {1569.05358},
url = {http://geodesic.mathdoc.fr/articles/10.37236/13248/}
}
TY - JOUR
AU - Timothy Y. Chow
AU - Mark G. Tiefenbruck
TI - The Latin tableau conjecture
JO - The electronic journal of combinatorics
PY - 2025
VL - 32
IS - 2
UR - http://geodesic.mathdoc.fr/articles/10.37236/13248/
DO - 10.37236/13248
ID - 10_37236_13248
ER -
%0 Journal Article
%A Timothy Y. Chow
%A Mark G. Tiefenbruck
%T The Latin tableau conjecture
%J The electronic journal of combinatorics
%D 2025
%V 32
%N 2
%U http://geodesic.mathdoc.fr/articles/10.37236/13248/
%R 10.37236/13248
%F 10_37236_13248
Timothy Y. Chow; Mark G. Tiefenbruck. The Latin tableau conjecture. The electronic journal of combinatorics, Tome 32 (2025) no. 2. doi: 10.37236/13248
