T. Hibi

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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 PlÃ¼cker ideals and algebras with straightening laws

Viktoriia Borovik, Takayuki Hibi

It is well known that the PlÃ¼cker ideal defining the Grassmannian is generated by quadratic PlÃ¼cker relations. These relations form a reverse lexicographic GrÃ¶bner basis and end…

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…