Positivity Results on Ribbon Schur Function Differences
Publication Date
2009
Description
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.
Journal
European Journal of Combinatorics
Volume
30
Issue
5
First Page
1352
Last Page
1369
Department
Mathematics
Link to Published Version
Recommended Citation
McNamara, Peter and van Willigenburg, Stephanie. "Positivity Results on Ribbon Schur Function Differences." European Journal of Combinatorics (2009) : 1352-1369.