2012 Fiscal Year Final Research Report
Topological combinatorics in the view of substructures and minimal counterexamples of simplicial complexes
| Project/Area Number |
21740062
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Single-year Grants |
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| Research Field |
General mathematics (including Probability theory/Statistical mathematics)
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| Research Institution | University of Tsukuba |
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Principal Investigator |
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| Project Period (FY) |
2009 – 2012
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| Keywords | 単体的複体 / shellability / sequentially Cohen-Macaulay / partitonability / obstruction / flag complex / pure-skeleton |
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| Research Abstract |
This study aimed analyses of combinatorial properties of simplicial complexes based on the structural analysis of substructures and minimal counterexamples. Especially, we studied shellability, sequential Cohen-Macaulayness, and partitionability, which play important roles in the study of topological combinatorics, and showed the counterexamples for these properties with respect to the restriction of the vertex set coincide for the class of simplicial complexes of dimension at most two, or in the class of flag complexes. We also studied the pure-skeletons of these counterexamples, and also proceeded some related applicational studies.
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