Several polytopes arise from finite graphs. For edge and symmetric edge polytopes, in particular, exhaustive computation of the Ehrhart polynomials not merely supports the conjecture of Beck et al.â€¦ (More)

An outstanding conjecture on roots of Ehrhart polynomials says that all roots Î± of the Ehrhart polynomial of an integral convex polytope of dimension d satisfy âˆ’d â‰¤ R(Î±) â‰¤ d âˆ’ 1. In this paper, weâ€¦ (More)

In this paper, we show that for given integers h and d with h > 1 and d > 3, there exists a non-normal very ample integral convex polytope of dimension d which has exactly h holes.

For an integral convex polytope P âŠ‚ R of dimension d, we call Î´(P) = (Î´0, Î´1, . . . , Î´d) the Î´-vector of P and vol(P) = âˆ‘d i=0 Î´i its normalized volume. In this paper, we will establish the newâ€¦ (More)

Abstract. Given arbitrary integers k and d with 0 â‰¤ 2k â‰¤ d, we construct a Gorenstein Fano polytope P âŠ‚ R of dimension d such that (i) its Ehrhart polynomial i(P , n) possesses d distinct roots; (ii)â€¦ (More)

Gorenstein Fano polytopes arising from finite partially ordered sets will be introduced. Then we study the problem which partially ordered sets yield smooth Fano polytopes.

In this paper, we consider the normality or the integer decomposition property (IDP, for short) for Minkowski sums of integral convex polytopes. We discuss some properties on the toric ringsâ€¦ (More)