T. Hibi

activity

20242026

collaborators

16 papers

math.AC2026

Bounded powers of edge ideals: Nearly Gorenstein polytopes

Takayuki Hibi, Seyed Amin Seyed Fakhari

A lattice polytope $P \subset R^{n}$ of dimension $n$ is called nearly Gorenstein if $P$ is normal and if its Ehrhart ring is a nearly Gorenstein ring. W…

math.AC2026

Componentwise linear monomial ideals

Takayuki Hibi, Seyed Amin Seyed Fakhari

Let $S = K [x_{1}, \dots, x_{n}]$ denote the polynomial ring in $n$ variables over a field $K$ with $deg x_{1} = \dots = deg x_{n} = 1$ and ${\bf a} = (a_1,\ldots,a_n) \in {\mathbb Z…

math.AC2026

Regularity and depth of binomial ideals arising from combinatorics

Takayuki Hibi, Seyed Amin Seyed Fakhari

Regularity and depth of binomial ideals generated by adjacent $2$ -minors together with those arising from finite lattices are studied.

math.AC2026

Partially ordered sets of distributive type and algebras with straightening laws

Takayuki Hibi, Seyed Amin Seyed Fakhari

A finite poset (partially ordered set) $P$ with $0^$ is called of distributive type if every interval $[0^, a]$ , $a \in P$ , of $P$ is a distributive lattice. From a vie…

math.AC2026

Characterization of Some Graphs Realizing Regularity Bounds for Binomial Edge Ideals

Nursel Erey, Muhammed Ergen, Takayuki Hibi

In this paper, we characterize all graphs $G$ satisfying \[\operatorname{reg}(S/J_G)=\ell(G)=c(G)\] where $ℓ (G)$ is the sum of the lengths of the longest induced paths in each c…

math.AC2026

Elimination ideals of Plücker ideals and algebras with straightening laws

Viktoriia Borovik, Takayuki Hibi

It is well known that the Plücker ideal defining the Grassmannian is generated by quadratic Plücker relations. These relations form a reverse lexicographic Gröbner basis and endow…

math.AC2025

Bounded powers of edge ideals: Pseudo-Gorenstein and Level polytopes

Takayuki Hibi, Seyed Amin Seyed Fakhari

A lattice polytope $P \subset R^{n}$ of dimension $n$ is called level* if (i) $P$ is normal, (ii) $(\mathcal{P} \setminus \partial \mathcal{P}) \cap \mat…

math.AC2025

Bounded powers of edge ideals: Gorenstein polytopes

Takayuki Hibi, Seyed Amin Seyed Fakhari

Let $S = K [x_{1}, \dots, x_{n}]$ denote the polynomial ring in $n$ variables over a field $K$ and $I (G) \subset S$ the edge ideal of a finite graph $G$ on $n$ vertices. Given a vector $\…

math.AC2025

Monomial curves and locally linear resolution

Takayuki Hibi, Peter Schenzel

For four elements of a Noetherian ring we construct complexes of free modules of length three (resp. five) by an explicit description of the homomorphisms of the free modules. We p…

math.AC2025

Bounded powers of edge ideals: symmetric exchange binomials

Takayuki Hibi, Seyed Amin Seyed Fakhari

It has been conjectured that the toric ideal of the base ring of a discrete polymatroid is generated by symmetric exchange binomials. In the present paper, we give several classes…

math.AC2025

Bounded powers of edge ideals: The strong exchange property

Takayuki Hibi, Seyed Amin Seyed Fakhari

Let $S = K [x_{1}, \dots, x_{n}]$ denote the polynomial ring in $n$ variables over a field $K$ and $I \subset S$ a monomial ideal. Given a vector $c \in Z_{> 0}^{n}$ , the i…

math.AC2025

Bounded powers of edge ideals: Gorenstein toric rings

Takayuki Hibi, Seyed Amin Seyed Fakhari

Let $S = K [x_{1}, \dots, x_{n}]$ denote the polynomial ring in $n$ variables over a field $K$ and $I \subset S$ a monomial ideal. Given a vector $c \in N^{n}$ , the ideal…

math.AC2025

Density of linearity index in the interval of matching numbers

Nursel Erey, Takayuki Hibi

Given integers $2 \leq p \leq c \leq q$ , we construct a finite simple graph $G$ with $ν_{1} (G) = p$ and $ν (G) = q$ for which the squarefree power $I (G)^{[k]}$ of the edge ideal $I(G)…

math.AC2025

Bounded powers of edge ideals: regularity and linear quotients

Takayuki Hibi, Seyed Amin Seyed Fakhari

Let $S = K [x_{1}, \dots, x_{n}]$ denote the polynomial ring in $n$ variables over a field $K$ and let $I \subset S$ be a monomial ideal. For a vector $c \in N^{n}$ , we se…

math.CO2024

Lattice polytopes with the minimal volume

Ginji Hamano, Ichiro Sainose, Takayuki Hibi

Let $P \subset R^{d}$ be a lattice polytope of dimension $d$ . Let $b (P)$ denote the number of lattice points belonging to the boundary of $P$ a…

math.CO2024

Diameter and connectivity of finite simple graphs II

Takayuki Hibi, Sara Saeedi Madani

Let $G$ be a finite simple non-complete connected graph on $[n] = {1, \dots, n}$ and $κ (G) \geq 1$ its vertex connectivity. Let $f (G)$ denote the number of free vertices of $G$ …