A Young diagram $Y$ is called wide if every sub-diagram $Z$ formed by a subset of the rows of $Y$ dominates $Z'$, the conjugate of $Z$. A Young diagram $Y$ is called Latin if its squares can be assigned numbers so that for each $i$, the $i$th row is filled injectively with the numbers $1, \ldots ,a_i$, where $a_i$ is the length of $i$th row of $Y$, and every column is also filled injectively. A conjecture of Chow and Taylor, publicized by Chow, Fan, Goemans, and Vondrak is that a wide Young diagram is Latin. We prove a dual version of the conjecture.

翻译：杨图$Y$称为宽杨图，若其任意行子集构成的子图$Z$均支配对偶图$Z'$。杨图$Y$称为拉丁杨图，若其方格可被赋值使得：对每个$i$，第$i$行被双射填充为数字$1,\ldots,a_i$（其中$a_i$为$Y$第$i$行的长度），且每列也为双射填充。Chow与Taylor提出、并经Chow、Fan、Goemans与Vondrak公开的猜想指出：宽杨图必为拉丁杨图。本文证明了该猜想的对偶版本。