Schur positivity of skew Schur function differences and applications to ribbons and Schubert classes
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- King, R.C., Welsh, T.A. & van Willigenburg, S.J. J Algebr Comb (2008) 28: 139. doi:10.1007/s10801-007-0113-0
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.