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arXiv · 0706.3253

Schur positivity of skew Schur function differences and applications to ribbons and Schubert classes

Ronald C. King·Trevor A. Welsh·Stephanie J. van Willigenburg
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Abstract

Some new relations on skew Schur function differences are established both combinatorially using Schützenberger's jeu de taquin, and algebraically using Jacobi-Trudi determinants. These relations lead to the conclusion that certain differences of skew Schur functions are Schur positive. Applying these results to a basis of symmetric functions involving ribbon Schur functions confirms the validity of a Schur positivity conjecture due to McNamara. A further application reveals that certain differences of products of Schubert classes are Schubert positive.

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Ronald C. King, Trevor A. Welsh, Stephanie J. van Willigenburg. 2007-12-14. Schur positivity of skew Schur function differences and applications to ribbons and Schubert classes. https://arxiv.org/abs/0706.3253

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