# Wide partition conjecture

**Conjecture**An integer partition is wide if and only if it is Latin.

An integer partition is *wide* if for every subpartition of . (Here denotes the conjugate of , denotes dominance or majorization order, and a subpartition of is a submultiset of the parts of .) An integer partition is *Latin* if there exists a tableau of shape such that for every , the th row of contains a permutation of , and such that every column of contains distinct integers. It is easy to show that if is Latin then is wide, but the converse remains open.

## Bibliography

*[CFGV] Timothy Y. Chow, C. Kenneth Fan, Michel X. Goemans, Jan Vondrak, Wide partitions, Latin tableaux, and Rota's basis conjecture, Advances Appl. Math. 21 (2003), 334-358.

* indicates original appearance(s) of problem.