Comparing skew Schur functions: a quasisymmetric perspectiveJournal of Combinatorics
AbstractReiner, Shaw and van Willigenburg showed that if two skew Schur functions sA and sB are equal, then the skew shapes $A$ and $B$ must have the same "row overlap partitions." Here we show that these row overlap equalities are also implied by a much weaker condition than Schur equality: that sA and sB have the same support when expanded in the fundamental quasisymmetric basis F. Surprisingly, there is significant evidence supporting a conjecture that the converse is also true. In fact, we work in terms of inequalities, showing that if the F-support of sA contains that of sB, then the row overlap partitions of A are dominated by those of B, and again conjecture that the converse also holds. Our evidence in favor of these conjectures includes their consistency with a complete determination of all F-support containment relations for F-multiplicity-free skew Schur functions. We conclude with a consideration of how some other quasisymmetric bases fit into our framework.
Citation InformationPeter R. W. McNamara. "Comparing skew Schur functions: a quasisymmetric perspective" Journal of Combinatorics (2014) p. 51 - 85
Available at: http://works.bepress.com/peter_mcnamara/25/