# Wide partition conjecture

 Importance: Medium ✭✭
 Author(s): Chow, Timothy Y. Taylor, Brian D.
 Subject: Combinatorics
 Keywords:
An integer partition $\lambda$ is \emph{wide} if $\mu \ge \mu'$ for every subpartition $\mu$ of $\lambda$. (Here $\mu'$ denotes the conjugate of $\mu$, $\ge$ denotes dominance or majorization order, and a subpartition of $\lambda$ is a submultiset of the parts of $\lambda$.) An integer partition $\lambda$ is \emph{Latin} if there exists a tableau $T$ of shape $\lambda$ such that for every $i$, the $i$th row of $T$ contains a permutation of $\{1,2,\ldots,\lambda_i\}$, and such that every column of $T$ contains distinct integers. It is easy to show that if $\lambda$ is Latin then $\lambda$ is wide, but the converse remains open.