Lattice polytopes from schur and symmetric grothendieck polynomials

Margaret Bayer, University of Kansas
Bennet Goeckner, University of Washington
Su Ji Hong, University of Nebraska–Lincoln
Tyrrell McAllister, University of Wyoming
McCabe Olsen, Hulman Institute of Technology
Casey Pinckney, Colorado State University
Julianne Vega, Kennesaw State University
Martha Yip, University of Kentucky


Given a family of lattice polytopes, two common questions in Ehrhart Theory are determining when a polytope has the integer decomposition property and determining when a polytope is reflexive. While these properties are of independent interest, the confluence of these properties is a source of active investigation due to conjectures regarding the unimodality of the h∗-polynomial. In this paper, we consider the Newton polytopes arising from two families of polynomials in algebraic combinatorics: Schur polynomials and inflated symmetric Grothendieck polynomi-als. In both cases, we prove that these polytopes have the integer decomposition property by using the fact that both families of polynomials have saturated Newton polytope. Furthermore, in both cases, we provide a complete characterization of when these polytopes are reflexive. We conclude with some explicit formulas and unimodality implications of the h∗-vector in the case of Schur polynomials.