Box Order and Dominance Order on Standard Young Tableaux

Abstract

We generalize results of [1] concerning two partial orders on Standard Young Tableaux: the dominance order and the box order. Extending their definitions from tableaux of a fixed shape to the set Tr of all Standard Young Tableaux of a fixed size r, we prove that these orders coincide in this more general setting. We also investigate basic properties of these orders. We further show that this result extends to Littlewood-Richardson tableaux whose skew shapes are rook strips. We briefly mention applications to invariant subspaces of nilpotent linear operators.

arXiv comment19 pages