Mathematics – Combinatorics
Scientific paper
2011-07-21
European Journal of Combinatorics, 33 (2012), 1190-1206
Mathematics
Combinatorics
24 pages, 4 figures. Incorporates referee's suggestions; to appear in the European Journal of Combinatorics
Scientific paper
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.
McNamara Peter R. W.
Willigenburg Stephanie van
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