Binomial edge ideals and conditional independence statements (2009)
Herzog, Juergen, Hibi, Takayuki, Hreinsdottir, Freyja, Kahle, Thomas, Rauh, Johannes
We introduce binomial edge ideals attached to a simple graph $G$ and study their algebraic properties. We characterize those graphs for which the quadratic generators form a Gr\"obner basis in a...
Smooth Fano polytopes arising from finite partially ordered sets (2009)
Hibi, Takayuki, Higashitani, Akihiro
Gorenstein Fano polytopes arising from finite partially ordered sets will be introduced. Then we study the problem which partially ordered sets yield smooth Fano polytopes.
Betti numbers of chordal graphs and $f$-vectors of simplicial complexes (2009)
Hibi, Takayuki, Kimura, Kyouko, Murai, Satoshi
Let $G$ be a chordal graph and $I(G)$ its edge ideal. Let $\beta (I(G)) = (\beta_0, \beta_1, ..., \beta_p)$ denote the Betti sequence of $I(G)$, where $\beta_i$ stands for the $i$th total Betti...
The toric ring and the toric ideal arising from a nested configuration (2009)
Ohsugi, Hidefumi, Hibi, Takayuki
The toric ring together with the toric ideal arising from a nested configuration is discussed. Especially, the algebraic study of normality of the toric ring as well as of Gr\"obner bases of the...
Powers of componentwise linear ideals (2009)
Herzog, Juergen, Hibi, Takayuki, Ohsugi, Hidefumi
We give criteria for graded ideals to have the property that all their powers are componentwise linear. Typical examples to which our criteria can be applied include the vertex cover ideals of...
Ehrhart polynomials of convex polytopes with small volumes (2009)
Hibi, Takayuki, Higashitani, Akihiro, Nagazawa, Yuuki
We classify all the possible $delta$-vectors of d-dimensional integral convex polytopes whose volumes are less than or equal to 3/(d!).
Very ample configurations arising from contingency tables (2009)
Ohsugi, Hidefumi, Hibi, Takayuki
In this paper, it is proved that, if a toric ideal possesses a fundamental binomial none of whose monomials is squarefree, then the corresponding semigroup ring is not very ample. Moreover, very...
reprint of the 1995 original. [353] (2009)
Ad S. Abeasis, A. Del Fra, Adk S. Abeasis, A. Del Fra, H. Kraft, Ab Valery Alexeev, ...
Numbers in square brackets at the end of each entry indicate the pages in the
Unmixed bipartite graphs and sublattices of the Boolean lattices (2008)
Herzog, Juergen, Hibi, Takayuki, Ohsugi, Hidefumi
The correspondence between unmixed bipartite graphs and sublattices of the oolean lattice is discussed. By using this correspondence, we show the existence of squarefree quadratic initial ideals of...
Simple polytopes arising from finite graphs (2008)
Ohsugi, Hidefumi, Hibi, Takayuki
Let $G$ be a finite graph allowing loops, having no multiple edge and no isolated vertex. We associate $G$ with the edge polytope ${\cal P}_G$ and the toric ideal $I_G$. By classifying graphs whose...
Hidefumi Ohsugi, Takayuki Hibi
The h-vector of a Gorenstein toric ring of
Groebner bases of nested configurations (2008)
Aoki, Satoshi, Hibi, Takayuki, Ohsugi, Hidefumi, Takemura, Akimichi
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-Veronese type will be...
Two way subtable sum problems and quadratic Groebner bases (2007)
Ohsugi, Hidefumi, Hibi, Takayuki
Hara, Takemura and Yoshida discuss toric ideals arising from two way subtable sum problems and shows that these toric ideals are generated by quadratic binomials if and only if the subtables are...
Linear balls and the multiplicity conjecture (2007)
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--Reisner ring of the...
Aoki, Satoshi, Hibi, Takayuki, Ohsugi, Hidefumi, Takemura, Akimichi
We consider testing independence in group-wise selections with some restrictions on combinations of choices. We present models for frequency data of selections for which it is easy to perform...
Vertex cover algebras of unimodular hypergraphs (2007)
Herzog, Jurgen, Hibi, Takayuki, Trung, Ngo Viet
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 powers of monomial...
Gotzmann ideals of the polynomial ring (2007)
Murai, Satoshi, Hibi, Takayuki
Let $A = K[x_1, ..., x_n]$ denote the polynomial ring in $n$ variables over a field $K$. We will classify all the Gotzmann ideals of $A$ with at most $n$ generators. In addition, we will study...
MATHEMATICAL ENGINEERING TECHNICAL REPORTS (2007)
Markov Basis, Gröbner Basis Of, Akimichi Takemura, Satoshi Aoki, Takayuki Hibi, Hidefumi Ohsugi, ...
Segre-Veronese configuration for testing independence in group-wise selections
Componentwise linear ideals with minimal or maximal Betti numbers (2006)
Herzog, Juergen, Hibi, Takayuki, Murai, Satoshi, Takayama, Yukihide
We characterize componentwise linear monomial ideals with minimal Taylor resolution and consider the lower bound for the Betti numbers of componentwise linear ideals.
The depth of an ideal with a given Hilbert function (2006)
Murai, Satoshi, Hibi, Takayuki
Let $A = K[x_1, ..., x_n]$ denote the polynomial ring in $n$ variables over a field $K$ with each $\deg x_i = 1$. Let $I$ be a homogeneous ideal of $A$ with $I \ne A$ and $H_{A/I}$ the Hilbert...
Herzog, Juergen, Hibi, Takayuki, Murai, Satoshi, Trung, Ngo Viet, Zheng, Xinxian
A forest is the clique complex of a strongly chordal graph and a quasi-forest is the clique complex of a chordal graph. Kruskal--Katona type theorems for forests, quasi-forests, pure forests and pure...
Standard graded vertex cover algebras, cycles and leaves (2006)
Herzog, Juergen, Hibi, Takayuki, Trung, Ngo Viet, Zheng, Xinxian
The aim of this paper is to characterize simplicial complexes which have standard graded vertex cover algebras. This property has several nice consequences for the squarefree monomial ideals defining...
Level rings arising from meet-distributive meet-semilattices (2006)
Herzog, Jürgen, Hibi, Takayuki
The homogenized ideal dual complex of an arbitrary meet-semilattice is introduced and described explicitly. Meet-distributive meet-semilattices whose homogenized ideal dual complex is level are...
Standard graded vertex cover algebras, cycles and leaves (2006)
Jürgen Herzog, Takayuki Hibi, Ngô Viêt Trung, Xinxian Zheng
This is a report on some results of a joint paper with the same title. Let ∆ be a simplicial complex on the vertex set [n] = {1,..., n}. Let F(∆) denote the set of the facets of ∆. We call an...
Symbolic powers of monomial ideals and vertex cover algebras (2005)
Herzog, Juergen, Hibi, Takayuki, Trung, Ngo Viet
We introduce and study vertex cover algebras of weighted simplicial complexes. These algebras are special classes of symbolic Rees algebras. We show that symbolic Rees algebras of monomial ideals are...
Ideals of fiber type and polymatroids (2005)
Herzog, Jürgen, Hibi, Takayuki, Vladoiu, Marius
In the first half of this paper, we complement the theory on discrete polymatroids. More precisely, (i) we prove that a discrete polymatroid satisfying the strong exchange property is, up to an...
Gin and Lex of certain monomial ideals (2005)
Murai, Satoshi, Hibi, Takayuki
Let $A = K[x_1, ..., x_n]$ denote the polynomial ring in $n$ variables over a field $K$ of characteristic 0 with each $\deg x_i = 1$. Given arbitrary integers $i$ and $j$ with $2 \leq i \leq n$ and...
Combinatorial shifting and graded Betti numbers (2005)
Murai, Satoshi, Hibi, Takayuki
This paper has been withdrawn since we combine this paper with math.AC/0503685. All contents of the paper have been moved to math.AC/0503685.
Special simplices and Gorenstein toric rings (2005)
Ohsugi, Hidefumi, Hibi, Takayuki
Christos Athanasiadis studies an effective technique to show that Gorenstein sequences coming from compressed polytopes are unimodal. In the present paper we will use such the technique to find a...
Algebraic shifting and graded Betti numbers (2005)
Hibi, Takayuki, Murai, Satoshi
Let $S = K[x_1, ..., x_n]$ denote the polynomial ring in $n$ variables over a field $K$ with each $\deg x_i = 1$. Let $\Delta$ be a simplicial complex on $[n] = \{1, ..., n \}$ and $I_\Delta \subset...
The depth of powers of an ideal (2004)
Herzog, Juergen, Hibi, Takayuki
We study the limit and initial behavior of the numerical function $f(k)=\depth S/I^k$. General properties of this function together with concrete examples arising from combinatorics are discussed.
Cohen-Macaulay Polymatroidal Ideals (2004)
Herzog, Juergen, Hibi, Takayuki
All Cohen--Macaulay polymatroidal ideals are classified. The Cohen--Macaulay polymatroidal ideals are precisely the principal ideals, the Veronese ideals, and the squarefree Veronese ideals.
Cohen-Macaulay chordal graphs (2004)
Herzog, Juergen, Hibi, Takayuki, Zheng, Xinxian
We classify all Cohen-Macaulay chordal graphs. In particular. it is shown that a chordal graph is Cohen-Macaulay if and only if its unmixed.
Level rings arising from meet-distributive meet-semilattices (2004)
Herzog, Juergen, Hibi, Takayuki
The Alexander dual of an arbitrary meet-semilattice is described explicitly. Meet-distributive meet-semilattices whose Alexander dual is level are characterized.
The monomial ideal of a finite meet-semilattice (2003)
Herzog, Juergen, Hibi, Takayuki, Zheng, Xinxian
Squarefree monomial ideals arising from finite meet-semilattices and their free resolutions are studied. For the squarefree monomial ideals corresponding to poset ideals in a distributive lattice the...
Distributive Lattices, Bipartite Graphs and Alexander Duality (2003)
Herzog, Juergen, Hibi, Takayuki
A certain squarefree monomial ideal $H_P$ arising from a finite partially ordered set $P$ will be studied from viewpoints of both commutative algebra and combinatorics. First, it is proved that the...
Herzog, Juergen, Hibi, Takayuki
The discrete polymatroid is a multiset analogue of the matroid. Based on the polyhedral theory on integral polymatroids developed in late 1960's and in early 1970's, in the present paper the...
Monomial ideals whose powers have a linear resolution (2003)
Herzog, Juergen, Hibi, Takayuki, Zheng, Xinxian
In this paper we consider graded ideals in a polynomial ring over a field and ask when such an ideal has the property that all of its powers have a linear resolution. In particular it is shown that...
Dirac's theorem on chordal graphs and Alexander duality (2003)
Herzog, Jürgen, Hibi, Takayuki, Zheng, Xinxian
By using Alexander duality on simplicial complexes we give a new and algebraic proof of Dirac's theorem on chordal graphs.
Rigid resolutions and big Betti numbers (2003)
Conca, Aldo, Herzog, Juergen, Hibi, Takayuki
In the first part of the paper we answer (positively) a question raised by the first author which has to do with some sort of rigity of the tail of resolution of an ideal. Let $I$ be a homogeneous...
Shellability of semigroup rings (2002)
Aramova, Annetta, Herzog, Jürgen, Hibi, Takayuki
The concepts of $\Lambda$-shellability of locally finite posets as well as of extendable sequentially Koszul algebras will be introduced. It will be proved that the divisor poset of a homogeneous...
Componentwise linear ideals (1999)
Herzog, Jürgen, Hibi, Takayuki
A componentwise linear ideal is a graded ideal $I$ of a polynomial ring such that, for each degree $q$, the ideal generated by all homogeneous polynomials of degree $q$ belonging to $I$ has a linear...
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