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Description: |
A symmetric function is said to be Schur positive (or nonnegative) if its expansion in the Schur basis has only nonnegative integer coefficients. In the recent years, several problems concerning the Schur positivity of certain differences of Schur function products of the form s_\rho s_\lambda−s_\mu s_\nu have been studied. In [Fomin, Fulton, Li, Poon , Amer. J. Math. 127 (2005) ] are made two conjectures on this subject: one of them was solved in [Lam, Postnikov, Pylyavskyy , Amer. J. Math. 129 (2007)], and, on the other one, some progress was made in [Bergeron, Biagioli and Rosas, J. Combin. Theory Ser. A 113 (2006)]. The talk focus the later conjecture in the case of multiplicity-free pairs of partitions (\mu,\nu). This is a joint work with M. Rosas, Universidad de Sevilla.
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