, Volume 28, Issue 1, pp 139-167
Date: 21 Dec 2007

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

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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.

For Manfred Schocker 1970–2006.
S.J. van Willigenburg was supported in part by the National Sciences and Engineering Research Council of Canada.