Pieri operators on posetsFrank SottileUniversity of Wisconsin & University of Massachusetts, Amherst
February 16,

ABSTRACT


Many enumeration problems in algebraic combinatorics lead to quasisymmetric generating functions, for example Schur functions, Ppartitions, and Stanley symmetric functions. Some of these have been shown to have interesting algebraic properties, most notably the Hopf structures of Ehrenborg's quasisymmetric generating function for the flag fvector 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 quasisymmetric functions. Our approach is motivated by work on the Schubert calculus for flag manifolds and uses representations of the algebra of noncommutative symmetric functions generated by what we call Pieri operators. 
Combinatorics Seminar, Mathematics Department, MIT, sara(atsign)math.mit.edu 

