Ehrhart polynomials of integral simplices with prime volumes

Abstract

For an integral convex polytope $\Pc \subset \RR^N$ of dimension $d$, we call $δ(\Pc)=(δ_0, δ_1,..., δ_d)$ the $\delta$-vector of $\Pc$ and $\vol(\Pc)=\sum_{i=0}^dδ_i$ its normalized volume. In this paper, we will establish the new equalities and inequalities on $\delta$-vectors for integral simplices whose normalized volumes are prime. Moreover, by using those, we will classify all the possible $\delta$-vectors of integral simplices with normalized volume 5 and 7.

11 pages

Cited by in corpus (1)

• On Ehrhart polynomials of lattice triangles