18 citations · 176 across the 52 of their papers we have counts for
57 papers
Magic positivity for polar duals of pseudo-symmetric smooth Fano polytopes
Hidefumi Ohsugi, Akiyoshi Tsuchiya
Motivated by Gal's conjecture, Ferroni and Higashitani conjectured that the -polynomial of any Gorenstein lattice polytope admitting a quadratic triangulation is -positive.…
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…
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…
Codegree and regularity of stable set polytopes
Koji Matsushita, Akiyoshi Tsuchiya
The codegree of a lattice polytope is a fundamental invariant in discrete geometry. In the present paper, we investigate the codegree of th…
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…
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…
PQ-type adjacency polytopes of join graphs
Hidefumi Ohsugi, Akiyoshi Tsuchiya
PQ-type adjacency polytopes are lattice polytopes arising from finite graphs . There is a connection between and the engineering problem…
Rigid Gorenstein toric Fano varieties arising from directed graphs
Selvi Kara, Irem Portakal, Akiyoshi Tsuchiya
A directed edge polytope is a lattice polytope arising from root system and a finite directed graph . If every directed edge of belongs to a directed c…
Edge rings with -linear resolutions
Kenta Mori, Hidefumi Ohsugi, Akiyoshi Tsuchiya
In the present paper, we give a complete classification of connected simple graphs whose edge rings have a -linear resolution with . In particular, we show that the ed…
Castelnuovo polytopes
Akiyoshi Tsuchiya
It is known that the sectional genus of a polarized variety has an upper bound, which is an extension of the Castelnuovo bound on the genus of a projective curve. Polarized varieti…
Symmetric edge polytopes and matching generating polynomials
Hidefumi Ohsugi, Akiyoshi Tsuchiya
Symmetric edge polytopes of type A are lattice polytopes arising from the root system and finite simple graphs . There is a connection between $\mathcal{A}…
Worpitzky-compatible subarrangements of braid arrangements and cocomparability graphs
Tan Nhat Tran, Akiyoshi Tsuchiya
The class of Worpitzky-compatible subarrangements of a Weyl arrangement together with an associated Eulerian polynomial was recently introduced by Ashraf, Yoshinaga and the first a…
Two enriched poset polytopes
Soichi Okada, Akiyoshi Tsuchiya
Stanley introduced and studied two lattice polytopes, the order polytope and chain polytope, associated to a finite poset. Recently Ohsugi and Tsuchiya introduce an enriched versio…
Odd cycles and Hilbert functions of their toric rings
Takayuki Hibi, Akiyoshi Tsuchiya
Studying Hilbert functions of concrete examples of normal toric rings, it is demonstrated that, for each , an -sequence $(h_0, h_1, \ldots, h_{2s-1}) \in \mathb…
An additive basis for the cohomology rings of regular nilpotent Hessenberg varieties
Makoto Enokizono, Tatsuya Horiguchi, Takahiro Nagaoka +1
In this paper we construct an additive basis for the cohomology ring of a regular nilpotent Hessenberg variety which is obtained by extending all Poincaré duals of smaller regular…
Uniform bases for ideal arrangements
Makoto Enokizono, Tatsuya Horiguchi, Takahiro Nagaoka +1
In this paper we introduce and study uniform bases for the ideal arrangements in all Lie types. Explicit uniform bases are given by Abe-Horiguchi-Masuda-Murai-Sato for types $A,B,C…
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…
Nef-partitions arising from unimodular configurations
Hidefumi Ohsugi, Akiyoshi Tsuchiya
Reflexive polytopes have been studied from viewpoints of combinatorics, commutative algebra and algebraic geometry. A nef-partition of a reflexive polytope is a decom…
Edge rings of bipartite graphs with linear resolutions
Akiyoshi Tsuchiya
Ohsugi and Hibi characterized the edge ring of a finite connected simple graph with a -linear resolution. On the other hand, Hibi, Matsuda and the author conjectured that the ed…
Depth of an initial ideal
Takayuki Hibi, Akiyoshi Tsuchiya
Given an arbitrary integer , we construct a homogeneous ideal of the polynomial ring in variables over a filed for which is a C…
The -polynomials of locally anti-blocking lattice polytopes and their -positivity
Hidefumi Ohsugi, Akiyoshi Tsuchiya
A lattice polytope is called a locally anti-blocking polytope if for any closed orthant in , $\mathcal…
Enriched order polytopes and Enriched Hibi rings
Hidefumi Ohsugi, Akiyoshi Tsuchiya
Stanley introduced two classes of lattice polytopes associated to posets, which are called the order polytope and the chain polytope of a poset $P…