65 citations · 613 across the 138 of their papers we have counts for
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The trace of the canonical module
Jürgen Herzog, Takayuki Hibi, Dumitru I. Stamate
The trace of the canonical module (the canonical trace) determines the non-Gorenstein locus of a local Cohen--Macaulay ring. We call a local Cohen--Macaulay ring nearly Gorenstein,…
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…
Markov bases for two-way change-point models of ladder determinantal tables
Satoshi Aoki, Takayuki Hibi
To evaluate a fitting of a statistical model to given data, calculating a conditional value by a Markov chain Monte Carlo method is one of the effective approaches. For this pu…
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…