%0 Journal Article
%T Maximal supports and Schur-positivity among connected skew shapes
%A Peter R. W. McNamara
%A Stephanie van Willigenburg
%J Mathematics
%D 2011
%I arXiv
%X The Schur-positivity order on skew shapes is defined by B \leq A if the difference s_A - s_B is Schur-positive. It is an open problem to determine those connected skew shapes that are maximal with respect to this ordering. A strong necessary condition for the Schur-positivity of s_A - s_B is that the support of B is contained in that of A, where the support of B is defined to be the set of partitions lambda for which s_lambda appears in the Schur expansion of s_B. We show that to determine the maximal connected skew shapes in the Schur-positivity order and this support containment order, it suffices to consider a special class of ribbon shapes. We explicitly determine the support for these ribbon shapes, thereby determining the maximal connected skew shapes in the support containment order.
%U http://arxiv.org/abs/1107.4373v2