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arXiv · 1107.4373

Maximal supports and Schur-positivity among connected skew shapes

Peter R. W. McNamara·Stephanie van Willigenburg
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Abstract

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.

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Peter R. W. McNamara, Stephanie van Willigenburg. 2011-07-21. Maximal supports and Schur-positivity among connected skew shapes. https://arxiv.org/abs/1107.4373

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