On Ehrhart Theory and Positivity

Abstract

We investigate the geometric and combinatorial properties of polytope triangulations, focusing on their connections to Ehrhart positivity. The Ehrhart polynomial L(P,t) encodes the number of integer points in dilated copies of a polytope, and establishing the positivity of the coefficients of L(P,t) remains a central and challenging problem in Ehrhart theory. To address this, we use unimodular triangulations to provide insight into the behavior of the polynomials' coefficients.

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