65 citations · 613 across the 138 of their papers we have counts for
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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…
Ehrhart series of fractional stable set polytopes of finite graphs
Ginji Hamano, Takayuki Hibi, Hidefumi Ohsugi
The fractional stable set polytope of a simple graph with vertices is a rational polytope that is the set of nonnegative vectors satisfyi…
A Gröbner basis characterization for chordal comparability graphs
Hidefumi Ohsugi, Takayuki Hibi
In this paper, we study toric ideals associated with multichains of posets. It is shown that the comparability graph of a poset is chordal if and only if there exists a quadratic G…