T. Hibi

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20242026

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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…