Roots of Ehrhart polynomials of Gorenstein Fano polytopes (2010)
Hibi, Takayuki, Higashitani, Akihiro, Ohsugi, Hidefumi
Given arbitrary integers $k$ and $d$ with $0 \leq 2k \leq d$, we construct a Gorenstein Fano polytope $\Pc \subset \RR^d$ of dimension $d$ such that (i) its Ehrhart polynomial $i(\Pc, n)$ possesses...
Shifted symmetric $\delta$-vectors of convex polytopes (2009)
A $\delta$-vector $\delta(\Pc)= (\delta_0, \delta_1, ..., \delta_d)$ is called shifted symmetric if $\delta_{d-i} = \delta_{i+1}$ for each $0 \leq i \leq [(d-1)/2]$. A natural family of...
Smooth Fano polytopes arising from finite partially ordered sets (2009)
Hibi, Takayuki, Higashitani, Akihiro
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.
Ehrhart polynomials of convex polytopes with small volumes (2009)
Hibi, Takayuki, Higashitani, Akihiro, Nagazawa, Yuuki
We classify all the possible $delta$-vectors of d-dimensional integral convex polytopes whose volumes are less than or equal to 3/(d!).