T. Hibi

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20242026

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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…