Ehrhart tensor polynomials

Abstract: An extension of the Ehrhart polynomial to tensor valuations on lattice polytopes is introduced. In particular, we initiate the study of the Ehrhart tensor polynomial, its coefficients, and its coefficients in a certain binomial basis - an extension of the $h^*$-polynomial. We will concentrate on the matrix case providing comparisons to classical Ehrhart theory. The reciprocity results of Ehrhart and MacDonald are extended, a Pick-type theorem is given, as is a result analagous to Stanley's nonnegativity. This is joint work with Monika Ludwig (TU Wien) and, separately, with Soren Berg (Fit Analytics) and Katharina Jochemko (KTH Stockholm).

combinatorics

Audience: researchers in the topic

New York combinatorics seminar