Takayuki Hibi

Prof. Takayuki Hibi

Department of Pure and Applied Mathematics, Graduate School of Information Science and Technology, Osaka University, 1-5 Yamadaoka, Suita 565-0871, Japan

Research Focus & Metrics

Academic Career Length

30Years (1997-Present)

(Calculated once Scilit publication data is synced: current year − year of first publication + 1)

Representative Publications

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1 January 1999 in Nagoya Mathematical Journal
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JHJürgen Herzog
Jürgen Herzog
Takayuki HibiTakayuki Hibi
Takayuki Hibi
A componentwise linear ideal is a graded ideal I of a polynomial ring such that, for each degreeq, the ideal generated by all homogeneous polynomials of degreeqbelonging toIhas a linear resolution. Examples of componentwise linear ideals include stable monomial ideals and Gotzmann ideals. The graded Betti numbers of a componentwise linear ideal can be determined by the graded Betti numbers of its components. Combinatorics on squarefree componentwise linear ideals will be especially studied. It turns out that the Stanley-Reisner idealIΔarising from a simplicial complex Δ is componentwise linear if and only if the Alexander dual of Δ is sequentially Cohen-Macaulay. This result generalizes the theorem by Eagon and Reiner which says that the Stanley-Reisner ideal of a simplicial complex has a linear resolution if and only if its Alexander dual is Cohen-Macaulay.

1 November 2005 in Journal of Algebraic Combinatorics
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JHJürgen Herzog
Jürgen Herzog
Takayuki HibiTakayuki Hibi
Takayuki Hibi

1 September 2004 in MATHEMATICA SCANDINAVICA
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JHJürgen Herzog
Jürgen Herzog
Takayuki HibiTakayuki Hibi
Takayuki Hibi
XZXinxian Zheng
Xinxian Zheng
Monomial ideals whose powers have a linear resolution

1 June 1998 in Mathematische Zeitschrift
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AAAnnetta Aramova
Annetta Aramova
JHJürgen Herzog
Jürgen Herzog
Takayuki HibiTakayuki Hibi
Takayuki Hibi

28 July 2008 in Transactions of the American Mathematical Society
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JHJürgen Herzog
Jürgen Herzog
Takayuki HibiTakayuki Hibi
Takayuki Hibi
NTNgô Viêt Trung
Ngô Viêt Trung
XZXinxian Zheng
Xinxian Zheng
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 these algebras. It turns out that such simplicial complexes are closely related to a range of hypergraphs which generalize bipartite graphs and trees. These relationships allow us to obtain very general results on standard graded vertex cover algebras which cover previous major results on Rees algebras of squarefree monomial ideals.

1 May 1997 in Journal of Algebra
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AAAnnetta Aramova
Annetta Aramova
JHJürgen Herzog
Jürgen Herzog
Takayuki HibiTakayuki Hibi
Takayuki Hibi