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16 papers · 1 filter
Binomial edge ideals and conditional independence statements
Juergen Herzog, Takayuki Hibi, Freyja Hreinsdottir +2
We introduce binomial edge ideals attached to a simple graph and study their algebraic properties. We characterize those graphs for which the quadratic generators form a Gröbne…
Groebner bases of nested configurations
Satoshi Aoki, Takayuki Hibi, Hidefumi Ohsugi +1
In this paper we introduce a new and large family of configurations whose toric ideals possess quadratic Groebner bases. As an application, a generalization of algebras of Segre-Ve…
Linear balls and the multiplicity conjecture
Takayuki Hibi, Pooja Singla
A linear ball is a simplicial complex whose geometric realization is homeomorphic to a ball and whose Stanley--Reisner ring has a linear resolution. It turns out that the Stanley--…
Vertex cover algebras of unimodular hypergraphs
Jurgen Herzog, Takayuki Hibi, Ngo Viet Trung
It is proved that all vertex cover algebras of a hypergraph are standard graded if and only if the hypergraph is unimodular. This has interesting consequences on the symbolic power…
Gotzmann ideals of the polynomial ring
Satoshi Murai, Takayuki Hibi
Let denote the polynomial ring in variables over a field . We will classify all the Gotzmann ideals of with at most generators. In addition, w…
Hilbert functions of d-regular ideals
Satoshi Murai
In the present paper, we characterize all possible Hilbert functions of graded ideals in a polynomial ring whose regularity is smaller than or equal to , where is a positive…