A new class of magic positive Ehrhart polynomials of reflexive polytopes

Abstract

The magic positivity of Ehrhart polynomials is a useful tool for proving the real-rootedness of the $h^{\ast }$-polynomials. In this paper, we provide a new class of reflexive polytopes whose Ehrhart polynomials are magic positive. First, we prove that the Ehrhart polynomials of Stasheff polytopes are magic positive. Second, we provide a partial proof of the magic positivity of the Ehrhart polynomials of the dual polytopes of the symmetric edge polytopes of cycles.

10 pages