To any skew shape A, we can associate the skew Schur function sA. We can then order the set of skew shapes by saying that A ≤ B if sA - sB is Schur-positive, i.e., when expanded in the basis of Schur functions, all the coefficients are non-negative. We call the resulting poset the Schur-positivity poset on skew shapes. While much recent work on Schur-positivity can be formulated in terms of the Schur-positivity poset, a complete understanding of the poset is presently well out of reach. After giving an introduction to the Schur-positivity poset, we show that restricting the skew shapes to the set of multiplicity-free ribbons yields a simple and appealing convex subposet.
This is joint work with Stephanie van Willigenburg