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Composition of transpositions and equality of ribbon Schur Q-functions

Research paper by Farzin Barekat, Stephanie van Willigenburg

Indexed on: 01 Sep '09Published on: 01 Sep '09Published in: Mathematics - Combinatorics



Abstract

We introduce a new operation on skew diagrams called composition of transpositions, and use it and a Jacobi-Trudi style formula to derive equalities on skew Schur Q-functions whose indexing shifted skew diagram is an ordinary skew diagram. When this skew diagram is a ribbon, we conjecture necessary and sufficient conditions for equality of ribbon Schur Q-functions. Moreover, we determine all relations between ribbon Schur Q-functions; show they supply a Z-basis for skew Schur Q-functions; assert their irreducibility; and show that the non-commutative analogue of ribbon Schur Q-functions is the flag h-vector of Eulerian posets.