Title

Maximal Supports and Schur-positivity Among Connected Skew Shapes

Publication Date

8-2012

Journal

European Journal of Combinatorics

Volume

33

Issue

6

First Page

1190

Last Page

1206

Abstract

The Schur-positivity order on skew shapes is defined by BA if the difference sAsB 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 sAsB 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 λ for which sλ appears in the Schur expansion of sB. 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.