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CAGE: Philadelphia Area Combinatorics and Alg. Geometry Seminar

Thursday, February 2, 2017 - 3:00pm

Dominic Searles

USC

Location

University of Pennsylvania

DRL 3C8

We introduce the combinatorial model of Kohnert tableaux, based on the diagram model of A. Kohnert. We use Kohnert tableaux to introduce the quasi-key basis of the polynomial ring, which lifts the quasi-Schur polynomials of Haglund, Luoto, Mason and van Willigenburg. Key polynomials expand positively in quasi-key polynomials which in turn expand positively in fundamental slide polynomials. We give simple combinatorial formulas for these expansions in terms of Kohnert tableaux, lifting the parallel expansions of a Schur polynomial into quasi-Schur polynomials into fundamental quasisymmetric polynomials. (Joint work with S. Assaf.)