8 papers
Algebraic aspects of unconditional lattice polytopes
Kenta Mori, Ryo Motomura, Hidefumi Ohsugi +1
Unconditional polytopes are convex polytopes that are symmetric with respect to all coordinate hyperplanes and arise naturally from anti-blocking polytopes by reflection. This pape…
Classification and counting of Gorenstein simplices with -polynomial
Akiyoshi Tsuchiya
Hibi, Yoshida, and the author classified Gorenstein simplices which are not lattice pyramids and whose \(h^*\)-polynomials are of the form \(1+t^k+t^{2k}+\cdots+t^{(v-1)k}\) when \…
Gorenstein Simplices and Even Binary Self-Complementary Codes
Akiyoshi Tsuchiya
It is known that if a Gorenstein simplex of dimension \(d\) and degree \(s\) is not a lattice pyramid, then \(d \leq 2s-1\). In this paper, we study the extremal case \(d=2s-1\). M…
Kempe equivalence and quadratic toric rings
Hidefumi Ohsugi, Akiyoshi Tsuchiya
Kempe equivalence is a classical and fundamental notion in graph coloring theory. In the present paper we establish a connection between Kempe equivalence and quadratic stable set…
Toric ideal of matching polytopes and edge colorings
Kenta Mori, Ryo Motomura, Hidefumi Ohsugi +1
In the present paper, we investigate the maximal degree of minimal generators of the toric ideal of the matching polytope of a graph. It is known that the toric ideal associated to…
Examining Kempe equivalence via commutative algebra
Hidefumi Ohsugi, Akiyoshi Tsuchiya
Kempe equivalence is a classical and important notion on vertex coloring in graph theory. In the present paper, we introduce several ideals associated with graphs and provide a met…