Discoveries / combinatorics

Real-Rootedness of Ehrhart h*-Polynomials at Large Width

A question of Averkov, Hofscheier and Nill on whether the Ehrhart $h^*$-polynomial of a lattice polytope of large lattice width is real-rooted. Proved in fixed dimension for sufficiently large lattice width, giving strict log-concavity and unimodality of the $h^*$-vector, with the analogous statement for the local $h^*$-polynomial of a lattice simplex.