2007/10/14 by Martin Henk, Henk, Martin, Makoto Tagami +1
Mathematics · #11H06 #52B20 #52C07 #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Combinatorics (math.CO) #Commutative Algebra and Its Applications #FOS: Mathematics #Metric Geometry (math.MG)
paper · pdf · doi:10.48550/arxiv.0710.2665
openalex publication_date 2007/10/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We present lower bounds for the coefficients of Ehrhart polynomials of convex lattice polytopes in terms of their volume. Concerning the coefficients of the Ehrhart series of a lattice polytope we show that Hibi's lower bound is not true for lattice polytopes without interior lattice points. The counterexample is based on a formula of the Ehrhart series of the join of two lattice polytope. We also present a formula for calculating the Ehrhart series of integral dilates of a polytope.