Geodesic
Composition of transpositions and equality of ribbon Schur \(Q\)-functions
The electronic journal of combinatorics, Tome 16 (2009) no. 1
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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 ${\Bbb Z}$-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.
DOI : 10.37236/199
Classification : 05E10, 05A19, 05A17
Mots-clés : compositions, Eulerian posets, ribbons, Schur \(Q\)-functions, tableaux 
@article{10_37236_199,
     author = {Farzin Barekat and Stephanie van Willigenburg},
     title = {Composition of transpositions and equality of ribbon {Schur} {\(Q\)-functions}},
     journal = {The electronic journal of combinatorics},
     year = {2009},
     volume = {16},
     number = {1},
     doi = {10.37236/199},
     zbl = {1226.05256},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/199/}
}
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Farzin Barekat; Stephanie van Willigenburg. Composition of transpositions and equality of ribbon Schur \(Q\)-functions. The electronic journal of combinatorics, Tome 16 (2009) no. 1. doi: 10.37236/199

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