Positivity results on ribbon Schur function differences

Details Positivity results on ribbon Schur function differences Positivity results on ribbon Schur function differences

2007-12-14

arxiv.org/abs/0712.2424v2

European Journal of Combinatorics, 30 (5) (2009), 1352-1369

Mathematics

Combinatorics

20 pages, 5 figures. Minor expository changes. Final version, to appear in the European J. Combin.

Scientific paper

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.

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