2015 Fiscal Year Final Research Report
Face enumeration of convex polytopes and cell complexes
| Project/Area Number |
25400043
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Multi-year Fund |
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| Section | 一般 |
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| Research Field |
Algebra
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| Research Institution | Osaka University (2014-2015)
Yamaguchi University (2013) |
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Principal Investigator |
Murai Satoshi 大阪大学, 情報科学研究科, 准教授 (90570804)
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| Project Period (FY) |
2013-04-01 – 2016-03-31
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| Keywords | 凸多面体 / cd指数 / 三角形分割 / スタンレー・ライスナー環 |
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| Outline of Final Research Achievements |
In this research project, we study the face numbers of polytopes and cell complexes. The followings are main results of this project.
(1) We find new method to study the cd-index of a convex polytope by using commutative algebra, and by applying this new method, we find new upper bounds of the cd-index.
(2) We find new applications of polyhedral Morse inequality and graded Betti numbers to the study of face numbers of triangulated manifolds.
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| Free Research Field |
可換環論
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