Séminaire LaCIM: «Newton Polytopes in Algebraic Combinatorics»

Conférencière: Cara Monical (UIUC)

Abstract: A polynomial has saturated Newton polytope (SNP) if every lattice point in the convex hull of its exponent vectors corresponds to a monomial. We compile instances of SNP in algebraic combinatorics, and show the phenomenon is widespread in many of the polynomial families of interest. We also give explicit inequalities for the Newton polytope of the Schubert polynomials based on the diagram of the permutation.