18 citations · 176 across the 52 of their papers we have counts for
4 papers · 2 filters
Gorenstein properties and integer decomposition properties of lecture hall polytopes
Takayuki Hibi, McCabe Olsen, Akiyoshi Tsuchiya
Though much is known about -lecture hall polytopes, there are still many unanswered questions. In this paper, we show that -lecture hall polytopes satisfy the int…
Self dual reflexive simplices with Eulerian polynomials
Takayuki Hibi, McCabe Olsen, Akiyoshi Tsuchiya
A lattice polytope is called reflexive if its dual is a lattice polytope. The property that is unimodularly equivalent to $\mathcal{P…
Facets and volume of Gorenstein Fano polytopes
Takayuki Hibi, Akiyoshi Tsuchiya
It is known that every integral convex polytope is unimodularly equivalent to a face of some Gorenstein Fano polytope. It is then reasonable to ask whether every normal polytope is…
Flat -vectors and their Ehrhart polynomials
Takayuki Hibi, Akiyoshi Tsuchiya
We call the -vector of an integral convex polytope of dimension flat if the -vector is of the form , where . In this paper…