Journal of Algebraic Combinatorics

, Volume 28, Issue 1, pp 139–167

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

  • Ronald C. King
  • Trevor A. Welsh
  • Stephanie J. van Willigenburg
Article

DOI: 10.1007/s10801-007-0113-0

Cite this article as:
King, R.C., Welsh, T.A. & van Willigenburg, S.J. J Algebr Comb (2008) 28: 139. doi:10.1007/s10801-007-0113-0

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.

Keywords

Jacobi-Trudi determinant Jeu de taquin Ribbon Schubert calculus Schur positive Skew Schur function Symmetric function 

Copyright information

© Springer Science+Business Media, LLC 2007

Authors and Affiliations

  • Ronald C. King
    • 1
  • Trevor A. Welsh
    • 2
  • Stephanie J. van Willigenburg
    • 3
  1. 1.School of MathematicsUniversity of SouthamptonHampshireUK
  2. 2.Department of PhysicsUniversity of TorontoTorontoCanada
  3. 3.Department of MathematicsUniversity of British ColumbiaVancouverCanada

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