30 citations · 184 across the 67 of their papers we have counts for
4 papers · 2 filters
Roots of Ehrhart polynomials and symmetric -vectors
Akihiro Higashitani
The conjecture on roots of Ehrhart polynomials, stated by Matsui et al. \cite[Conjecture 4.10]{MHNOH}, says that all roots of the Ehrhart polynomial of a Gorenstein Fano polyto…
Ehrhart polynomials of integral simplices with prime volumes
Akihiro Higashitani
For an integral convex polytope $\Pc \subset \RR^N$ of dimension , we call $δ(\Pc)=(δ_0, δ_1,..., δ_d)$ the -vector of $\Pc$ and $\vol(\Pc)=\sum_{i=0}^dδ_i$ its normalized vo…
Counterexamples of the conjecture on roots of Ehrhart polynomials
Akihiro Higashitani
An outstanding conjecture on roots of Ehrhart polynomials says that all roots of the Ehrhart polynomial of an integral convex polytope of dimension satisfy $-d \leq \Re(α)…
Smooth Fano polytopes arising from finite directed graphs
Akihiro Higashitani
In this paper, we consider terminal reflexive polytopes arising from finite directed graphs and study the problem of deciding which directed graphs yield smooth Fano polytopes. We…