The Study of theoretical aspects and practical aspect on Grobner Bases

Grobner基底的理论与实践研究

• 批准号: 18340008
• 负责人: HIBI Takayuki
• 金额: $ 10.14万
• 依托单位: Osaka University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (B)
• 财政年份: 2006
• 资助国家: 日本
• 起止时间: 2006 至 2009
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-18340008/
• 关键词: グレブナー基底; 計算可換代数; 計算代数解析; 計算代数統計; 凸多面体; イニシャルイデアル; マルコフ基底; 分割表; アルゴリズム; トーリックイデアル; グレブナ-基底; D加群; generic initial ideal; 計算の効率化; 凸多面体の組合せ論

With taking the persistence and the internationalization into consideration, in collaboration with many researchers in various field including computational commutative algebra, computational algebraic analysis, computational algebraic statistics as well as algebraic algorithm, this research project strongly developed the study on the theoretical effectivity and practical effectivity of Grobner bases and succeeded in establishing the foundations of the modern theory of Grobner bases. At present, in order for our research group to be one of the strongest international footholds on the theoretical and practical research of Grobner bases, the CREST research project "Harmony of Grobner bases and the modern industry society," whose team leader is Takayuki Hibi, which is supported by JST (Japan Science and Technology Agency) follows this research project.

考虑到持久性和国际化的考虑，与许多领域的许多研究人员合作，包括计算交换代数，计算代数分析，计算代数统计以及代数算法，这项研究项目强烈发展了对Grobner Bases和Grobner Bases base base nosed in nosed nosed in nosed nosed noperty in nosed nosed noperty in nosed nosed nosed nosed nosed nopertion in nosed nosed nosed nosed nosed nosed nosed nosed nosed nosed nosed nosed nosed nosed nosed nosed nosed nosity in nosed nosed nosed nosity的研究的研究。目前，为了使我们的研究小组成为Grobner Bases的理论和实践研究的最强国际立足之一，Crest Research项目“ Grobner Bases和Modern Industry Society的Harmony of Grobner Base and Modern Industry Society”，其团队领导者是Takayuki Hibi，由JST（日本科学技术机构）支持该研究项目。

项目成果

Vertex cover algebras of unimodlar hypergraphs

单模超图的顶点覆盖代数

• 发表时间: 2009
• 期刊: Proc.Amer.Math.Soc. 137
• 作者: J.Herzong;日本孝之; N.V.Trung
• 通讯作者: N.V.Trung

rings arising from meet-distributive meet-semilattices

由相遇分布相遇半格产生的环

• 发表时间: 2006
• 期刊: Nagoya Math. J 181
• 作者: J. Herzog;T. Hibi
• 通讯作者: T. Hibi

Maximal Betti numbers of Cohen-Macaulay complexes with a given $f$-vector

具有给定 $f$-向量的 Cohen-Macaulay 复合体的最大 Betti 数

• 发表时间: 2007
• 期刊: Arch. Math 88
• 作者: S. Murai;T. Hibi
• 通讯作者: T. Hibi

Gin and lex of certain monomial ideals

某些单项式理想的 Gin 和 lex

• 发表时间: 2006
• 期刊: Math. Scand. 99
• 作者: Masaaki Katsuno;Denis Gleeson;Juergen Herzog;Juergen Herzog;Juergen Herzog;Satoshi Murai
• 通讯作者: Satoshi Murai

Grobner bases of nested configurations

嵌套配置的 Grobner 基

• 发表时间: 2008
• 期刊: J. Algebra 320
• 作者: S. Aoki;T. Hibi;H. Ohsugi;A. Takemura
• 通讯作者: A. Takemura