UBC Discrete Math Seminar: Dominic Searles

We establish a poset structure on combinatorial bases of polynomials, defined by positive expansions. These bases include the well-studied Schubert polynomials, Demazure characters and Demazure atoms, as well as the recently-introduced slide and quasi-key bases. The product of a Schur polynomial and an element of a basis in the poset expands positively in that basis; in particular we give the first Littlewood-Richardson rule for the product of a Schur polynomial and a quasi-key polynomial, extending the rule of Haglund, Luoto, Mason and van Willigenburg for quasi-Schur polynomials. We also establish bijections connecting combinatorial models for these polynomials, including semi-skyline fillings and quasi-key tableaux.