2019 Fiscal Year Final Research Report
Analysis of Cayley decomposition of integral convex polytopes and solutions of related problems
| Project/Area Number |
17K14177
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Multi-year Fund |
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| Research Field |
Algebra
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| Research Institution | Osaka University (2019)
Kyoto Sangyo University (2017-2018) |
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Principal Investigator |
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| Project Period (FY) |
2017-04-01 – 2020-03-31
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| Keywords | 整凸多面体 / Cayley分解 / Ehrhart多項式 |
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| Outline of Final Research Achievements |
The main purpose of this research project is the analysis of the combinatorial structure of Cayley decompositions of integral convex polytopes. As concrete problems, the complete solution of "Cayley conjecture" and the investigation of the relationship between Ehrhart polynomials and Cayley decompositions of integral convex polytopes are investigated.
Integral convex polytopes are a mathematical object appearing in various branches. The purpose of this research project is to a deep approach to the essence of Cayley decompositions of integral convex polytopes, which are one of the most essential structure of integral convex polytopes.
As the results of this project for three years, five research articles have been written and six research talks have been given.
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| Free Research Field |
代数的組合せ論
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| Academic Significance and Societal Importance of the Research Achievements |
本研究は、整凸多面体に関する研究の一種である。整凸多面体とは、例えば「ナップサック問題」と呼ばれる整数計画問題の文脈でも現れる対象であり、応用数学などにおける分野でも非常に重要な対象として知られている。
３年間実施した本研究は、整凸多面体の「Cayley分解」と呼ばれる特殊な構造の有無に注目し、様々な研究を展開した。今後は、本研究の成果を元に、整数計画問題への応用も見据えた研究が可能となる。
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