Abstract:
A polynomial has saturated Newton polytope (SNP) if every lattice point of the convex hull of its exponent vectors corresponds to a monomial. In combinatorics, many polynomials have this property, such as Schur polynomials, Schubert polynomials, key polynomials, Macdonald polynomials and so on. In this talk, I will investigate the SNP property of skew Schur polynomials, dual -Schur polynomials, affine Stanley symmetric polynomials and truncated determinants of Jacobi-Trudi matrices. This series of work is joint with Bo Wang, Arthur L.B. Yang, Philip B. Zhang, and Zhong-Xue Zhang.