17 citations · 55 across the 7 of their papers we have counts for
8 papers
Gröbner bases of toric ideals associated with matroids
Ken-ichi Hayase, Takayuki Hibi, Koyo Katsuno +1
In 1980, White conjectured that the toric ideal of a matroid is generated by quadratic binomials corresponding to a symmetric exchange. In this paper, we compute Gröbner bases of t…
Perfectly contractile graphs and quadratic toric rings
Hidefumi Ohsugi, Kazuki Shibata, Akiyoshi Tsuchiya
Perfect graphs form one of the distinguished classes of finite simple graphs. In 2006, Chudnovsky, Robertson, Seymour and Thomas proved that a graph is perfect if and only if it ha…
Toric rings and ideals of stable set polytopes
Kazunori Matsuda, Hidefumi Ohsugi, Kazuki Shibata
In this paper, we discuss the normality of the toric rings of stable set polytopes, and the set of generators and Gröbner bases of toric ideals of stable set polytopes by using the…
Strong Koszulness of the toric ring associated to a cut ideal
Kazuki Shibata
A cut ideal of a graph was introduced by Sturmfels and Sullivant. In this paper, we give a necessary and sufficient condition for toric rings associated to the cut ideal to be Stro…
Centrally symmetric configurations of order polytopes
Takayuki Hibi, Kazunori Matsuda, Hidefumi Ohsugi +1
It is shown that the toric ideal of the centrally symmetric configuration of the order polytope of a finite partially ordered set possesses a squarefree quadratic initial ideal. It…
Toric ideals of series and parallel connections of matroids
Kazuki Shibata
In 1980, White conjectured that the toric ideal associated to a matroid is generated by binomials corresponding to a symmetric exchange. In this paper, we prove that classes of mat…
Roots of the Ehrhart polynomial of hypersimplices
Hidefumi Ohsugi, Kazuki Shibata
The Ehrhart polynomial of the -th hypersimplex of order is studied. By computational experiments and a known result for , we conjecture that the real part of e…
Smooth Fano polytopes whose Ehrhart polynomial has a root with large real part
Hidefumi Ohsugi, Kazuki Shibata
The symmetric edge polytopes of odd cycles (del Pezzo polytopes) are known as smooth Fano polytopes. In this paper, we show that if the length of the cycle is 127, then the Ehrhart…