Necessary Conditions for Schur-Positivity

Details Necessary Conditions for Schur-Positivity Necessary Conditions for Schur-Positivity

2007-06-12

arxiv.org/abs/0706.1800v3

J. Algebraic Combin. 28 (4) (2008) 495-507

Mathematics

Combinatorics

12 pages, 4 figures. Fixed typos; final version. To appear in the Journal of Algebraic Combinatorics

Scientific paper

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.

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