Positivity results on ribbon Schur function differences

Authors:
Peter R. W. McNamara;Stephanie van Willigenburg
Affiliations:
Department of Mathematics, Bucknell University, Lewisburg, PA 17837, USA;Department of Mathematics, University of British Columbia, Vancouver, BC V6T 1Z2, Canada
Venue:
European Journal of Combinatorics
Year:
2009

Citing 4
Cited 1

Enumerative combinatorics

Enumerative combinatorics
Inequalities between Littlewood-Richardson coefficients

Journal of Combinatorial Theory Series A
Schur positivity of skew Schur function differences and applications to ribbons and Schubert classes

Journal of Algebraic Combinatorics: An International Journal
Necessary conditions for Schur-positivity

Journal of Algebraic Combinatorics: An International Journal

Maximal supports and Schur-positivity among connected skew shapes

European Journal of Combinatorics

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Abstract

There is considerable current interest in determining when the difference of two skew Schur functions is Schur positive. We consider the posets that result from ordering skew diagrams according to Schur positivity, before focussing on the convex subposets corresponding to ribbons. While the general solution for ribbon Schur functions seems out of reach at present, we determine necessary and sufficient conditions for multiplicity-free ribbons, i.e. those whose expansion as a linear combination of Schur functions has all coefficients either zero or one. In particular, we show that the poset that results from ordering such ribbons according to Schur positivity is essentially a product of two chains.