2017 Fiscal Year Final Research Report
Analysis of the structure of simplicial complexes based on the homogenity of substructures
| Project/Area Number |
25400191
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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 |
Foundations of mathematics/Applied mathematics
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| Research Institution | University of Tsukuba |
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Principal Investigator |
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| Project Period (FY) |
2013-04-01 – 2018-03-31
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| Keywords | 単体的複体 / shellable / Cohen-Macaulay / partitionable / マトロイド / トポロジー的組合せ論 |
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| Outline of Final Research Achievements |
This work studied, as one of the topics of topological combinatorics, the structures of simplicial complexes whose all substructures homogeneously have the same property. The main topic is related to shellability, sequentially Cohen-Macaulayness, and partitionability, and our interest is in the structures of simplicial complexes all of whose substructures hereditarily satisfy these properties. As one of our results, we proposed a new property that is a weak version of nonnegativity of h-triangles, and showed the relations between this property and the above three properties when hereditarity is required. We also discussed the hereditary property of shellability etc. can be seen as generalizations of matroids,
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| Free Research Field |
組合せ論、離散数学、トポロジー的組合せ論
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