Study on open problems arising from convex polytopes with strategies of the developed theory of Groebner bases

2014 Fiscal Year Final Research Report

• Project/Area Number: 22340008
• Research Category: Grant-in-Aid for Scientific Research (B)
• Allocation Type: Single-year Grants
• Section: 一般
• Research Field: Algebra
• Research Institution: Osaka University
• Principal Investigator: HIBI Takayuki 大阪大学, 情報科学研究科, 教授 (80181113)
• Co-Investigator(Renkei-kenkyūsha): OHSUGI Hidefumi 関西学院大学, 理工学部, 教授 (80350289) ; MURAI Satoshi 大阪大学, 大学院情報科学研究科, 准教授 (90570804)
• Project Period (FY): 2010-04-01 – 2015-03-31
• Keywords: グレブナー基底 / 凸多面体 / 単項式イデアル / ファノ凸多面体 / 有限グラフ / 辺イデアル / 二項式辺イデアル

Outline of Final Research Achievements

Following our current study on Groebner bases, we evolved the modern theory of Groebner bases and broke original techniques to discover new Groebner bases. As a result, we succeeded in developing remarkably the algebraic combinatorics on convex polytopes as well as the theory of monomial ideals in commutative algebra. Especially, new classes of Gorenstein Fano polytopes were created, and the regularity of edge ideals of finite graphs was deeply studied. Furthermore, the concept of binomial edge ideals of finite graphs was introduced and its fundamental theory was established.

Free Research Field

計算可換代数と組合せ論