Composition of transpositions and equality of ribbon Schur Q-functions

Details Composition of transpositions and equality of ribbon Schur Q-functions Composition of transpositions and equality of ribbon Schur Q-functions

2008-11-24

arxiv.org/abs/0811.3801v2

Electron. J. Combin. 16:R110 (2009)

Mathematics

Combinatorics

27 pages; final version to appear in Electron. J. Combin

Scientific paper

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.

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