Necessary Conditions for Schur-Positivity
arXiv:0706.1800
Abstract
In recent years, there has been considerable interest in showing that certain conditions on skew shapes A and B are sufficient for the difference s_A - s_B of their skew Schur functions to be Schur-positive. We determine necessary conditions for the difference to be Schur-positive. Our conditions are motivated by those of Reiner, Shaw and van Willigenburg that are necessary for s_A = s_B, and we deduce a strengthening of their result as a special case.
12 pages, 4 figures. Fixed typos; final version. To appear in the Journal of Algebraic Combinatorics