Pieri operators on posets

Frank Sottile

University of Wisconsin & University of Massachusetts, Amherst

February 16,
refreshments at 3:45pm


Many enumeration problems in algebraic combinatorics lead to quasi-symmetric generating functions, for example Schur functions, P-partitions, and Stanley symmetric functions. Some of these have been shown to have interesting algebraic properties, most notably the Hopf structures of Ehrenborg's quasi-symmetric generating function for the flag f-vector of a polytope and Bergeron and Sottile's generating function for descents in a labeled poset.

This talk will describe joint work with Bergeron, Mykytiuk, and van Willigenburg which gives a unified construction of many such quasi-symmetric functions. Our approach is motivated by work on the Schubert calculus for flag manifolds and uses representations of the algebra of non-commutative symmetric functions generated by what we call Pieri operators.

Speaker's Contact Info: sottile(at-sign)math.wisc.edu

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Combinatorics Seminar, Mathematics Department, MIT, sara(at-sign)math.mit.edu

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