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

King, Ronald C., Welsh, Trevor A. and van Willigenberg, Stephanie J. (2008) Schur positivity of skew Schur function differences and applications to ribbons and Schubert classes Journal of Algebraic Combinatorics, 28, pp. 139-167. (doi:10.1007/s10801-007-0113-0).

Record type: Article


Some new relations on skew Schur function differences are established both combinatorially using Sch\"utzenberger'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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Published date: August 2008
Keywords: jacobi-trudi determinant, jeu de taquin, ribbon, schubert calculus, schur positive, skew schur function, symmetric function


Local EPrints ID: 66210
ISSN: 0925-9899
PURE UUID: 239e33bf-6c5b-4b0d-976a-111715fa8fac

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Date deposited: 12 Jan 2010
Last modified: 19 Jul 2017 00:26

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Author: Ronald C. King
Author: Trevor A. Welsh
Author: Stephanie J. van Willigenberg

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