Kazunori Matsuda

activity

20122025

most citedCentrally symmetric configurations of order polytopes

14 citations · 82 across the 27 of their papers we have counts for

collaborators

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23 papers · 1 filter

math.AC2021

Inequalities of invariants on Stanley-Reisner rings of Cohen-Macaulay simplicial complexes

Akihiro Higashitani, Hiroju Kanno, Kazunori Matsuda

The goal of the present paper is the study of some algebraic invariants of Stanley-Reisner rings of Cohen-Macaulay simplicial complexes of dimension $d - 1$ . We prove that the ineq…

math.AC2020★ 1 cited

Homological invariants of Cameron--Walker graphs

Takayuki Hibi, Hiroju Kanno, Kyouko Kimura +2

Let $G$ be a finite simple connected graph on $[n]$ and $R = K [x_{1}, \dots, x_{n}]$ the polynomial ring in $n$ variables over a field $K$ . The edge ideal of $G$ is the ideal $I (G)$ o…

math.AC2020

Matching numbers and dimension of edge ideals

Ayana Hirano, Kazunori Matsuda

Let $G$ be a finite simple graph on the vertex set $V (G) = {x_{1}, \dots, x_{n}}$ and match $(G)$ , min-match $(G)$ and ind-match $(G)$ the matching number, minimum matching number…

math.AC2019★ 3 cited

Induced matching numbers of finite graphs and edge ideals

Takayuki Hibi, Hiroju Kanno, Kazunori Matsuda

Let $G$ be a finite simple graph on the vertex set $V (G) = {x_{1}, \dots, x_{n}}$ and $I (G) \subset K [V (G)]$ its edge ideal, where $K [V (G)]$ is the polynomial ring in $x_1, \ldots,…

math.AC2019★ 14 cited

Regularity and $a$ -invariant of Cameron--Walker graphs

Takayuki Hibi, Kyouko Kimura, Kazunori Matsuda +1

Let $S$ be the polynomial ring over a field $K$ and $I \subset S$ a homogeneous ideal. Let $h (S / I, λ)$ be the $h$ -polynomial of $S / I$ and $s = deg h (S / I, λ)$ the degree of $…

math.AC2018★ 1 cited

Regularity and $h$ -polynomials of edge ideals

Takayuki Hibi, Kazunori Matsuda, Adam Van Tuyl

For any two integers $d, r \geq 1$ , we show that there exists an edge ideal $I (G)$ such that the $reg (R / I (G))$ , the Castelnuovo-Mumford regularity of $R / I (G)$ , is $…

math.AC2018

Extremal Betti numbers of edge ideals

Takayuki Hibi, Kyouko Kimura, Kazunori Matsuda

Given integers $r$ and $b$ with $1 \leq b \leq r$ , a finite simple connected graph $G$ for which $reg (S / I (G)) = r$ and the number of extremal Betti numbers of $S / I (G)$ is equ…

math.AC2018★ 7 cited

Regularity and h-polynomials of binomial edge ideals

Takayuki Hibi, Kazunori Matsuda

Let $G$ be a finite simple graph on the vertex set $[n] = {1, \dots, n}$ and $K [X, Y] = K [x_{1}, \dots, x_{n}, y_{1}, \dots, y_{n}]$ the polynomial ring in $2 n$ variables over a fie…

math.AC2018★ 1 cited

Lexsegment ideals and their h-polynomials

Takayuki Hibi, Kazunori Matsuda

Let $S = K [x_{1}, \dots, x_{n}]$ denote the polynomial ring in $n$ variables over a field $K$ with each $deg x_{i} = 1$ and $I \subset S$ a homogeneous ideal of $S$ with $\dim…

math.AC2017★ 10 cited

Edge rings with $3$ -linear resolutions

Takayuki Hibi, Kazunori Matsuda, Akiyoshi Tsuchiya

It is shown that the edge ring of a finite connected simple graph with a $3$ -linear resolution is a hypersurface.

math.AC2017

Regularity and $h$ -polynomials of monomial ideals

Takayuki Hibi, Kazunori Matsuda

Let $S = K [x_{1}, \dots, x_{n}]$ denote the polynomial ring in $n$ variables over a field $K$ with each $° x_{i} = 1$ and $I \subset S$ a homogeneous ideal of $S$ with $dim S / I = d$ . Th…

math.AC2016

Non-Koszul quadratic Gorenstein toric rings

Kazunori Matsuda

Koszulness of Gorenstein quadratic algebras of small socle degree is studied. In this note, we construct non-Koszul Gorenstein quadratic toric ring such that its socle degree is mo…

math.AC2016★ 1 cited

Nonincreasing depth functions of monomial ideals

Kazunori Matsuda, Tao Suzuki, Akiyoshi Tsuchiya

Given a nonincreasing function $f : Z_{\geq 0} ∖ {0} \to Z_{\geq 0}$ such that (i) $f (k) - f (k + 1) \leq 1$ for all $k \geq 1$ and (ii) if $a = f (1)$ an…

math.AC2016★ 9 cited

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…

math.AC2015★ 5 cited

Quadratic Gröbner bases arising from partially ordered sets

Takayuki Hibi, Kazunori Matsuda, Akiyoshi Tsuchiya

The order polytope $O (P)$ and the chain polytope $C (P)$ associated to a partially ordered set $P$ are studied. In this paper, we introduce the convex polytope $…

math.AC2015★ 4 cited

Quadratic Gröbner bases of twinned order polytopes

Takayuki Hibi, Kazunori Matsuda

Let $P$ and $Q$ be finite partially ordered sets on $[d] = {1, \dots, d}$ , and $O (P) \subset R^{d}$ and $O (Q) \subset R^{d}$ their order po…

math.AC2014★ 14 cited

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…

math.AC2014★ 1 cited

Reverse lexicographic Gröbner bases and strongly Koszul toric rings

Kazunori Matsuda, Hidefumi Ohsugi

Restuccia and Rinaldo proved that a standard graded $K$ -algebra $K [x_{1}, ... x_{n}] / I$ is strongly Koszul if the reduced Gröbner basis of $I$ with respect to any reverse lexicographic…

math.AC2013

Strongly Koszul edge rings

Takayuki Hibi, Kazunori Matsuda, Hidefumi Ohsugi

We classify the finite connected simple graphs whose edge rings are strongly Koszul. From the classification, it follows that if the edge ring is strongly Koszul, then its toric id…

math.AC2013★ 1 cited

Strong Koszulness of toric rings associated with stable set polytopes of trivially perfect graphs

Kazunori Matsuda

We give necessary and sufficient conditions for strong Koszulness of toric rings associated with the stable set polytope of graphs.

math.AC2012★ 9 cited

Weakly closed graphs and F-purity of binomial edge ideals

Kazunori Matsuda

Herzog-Hibi-Hreindóttir-Kahle-Rauh introduced the class of closed graph and they proved that the binomial edge ideal $J (G)$ of a graph $G$ has quadratic Gröbner bases if $G$ is clo…

math.AC2012★ 1 cited

Regularity bounds for binomial edge ideals

Kazunori Matsuda, Satoshi Murai

We show that the Castelnuovo-Mumford regularity of the binomial edge ideal of a graph is bounded below by the length of its longest induced path and bounded above by the number of…

math.AC2012

Diagonal F-thresholds and F-pure thresholds of Hibi rings

Takahiro Chiba, Kazunori Matsuda

Hibi rings are a kind of graded toric ring on a finite distributive lattice $D = J (P)$ , where $P$ is a partially ordered set. In this paper, we compute diagonal F-thresholds and F-…

Inequalities of invariants on Stanley-Reisner rings of Cohen-Macaulay simplicial complexes

Homological invariants of Cameron--Walker graphs

Matching numbers and dimension of edge ideals

Induced matching numbers of finite graphs and edge ideals

Regularity and a-invariant of Cameron--Walker graphs

Regularity and h-polynomials of edge ideals

Extremal Betti numbers of edge ideals

Regularity and h-polynomials of binomial edge ideals

Lexsegment ideals and their h-polynomials

Edge rings with 3-linear resolutions

Regularity and h-polynomials of monomial ideals

Non-Koszul quadratic Gorenstein toric rings

Nonincreasing depth functions of monomial ideals

Toric rings and ideals of stable set polytopes

Quadratic Gröbner bases arising from partially ordered sets

Quadratic Gröbner bases of twinned order polytopes

Centrally symmetric configurations of order polytopes

Reverse lexicographic Gröbner bases and strongly Koszul toric rings

Strongly Koszul edge rings

Strong Koszulness of toric rings associated with stable set polytopes of trivially perfect graphs

Weakly closed graphs and F-purity of binomial edge ideals

Regularity bounds for binomial edge ideals

Diagonal F-thresholds and F-pure thresholds of Hibi rings

Regularity and $a$ -invariant of Cameron--Walker graphs

Regularity and $h$ -polynomials of edge ideals

Edge rings with $3$ -linear resolutions

Regularity and $h$ -polynomials of monomial ideals