18 citations · 176 across the 52 of their papers we have counts for
10 papers · 1 filter
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…
Regularity and -invariant of Cameron--Walker graphs
Takayuki Hibi, Kyouko Kimura, Kazunori Matsuda +1
Let be the polynomial ring over a field and a homogeneous ideal. Let be the -polynomial of and the degree of $…