2015 Fiscal Year Final Research Report
Algebraic combinatorics from the viewpoint of finite sets on a sphere
| Project/Area Number |
25800011
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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 | Aichi University of Education |
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Principal Investigator |
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| Project Period (FY) |
2013-04-01 – 2016-03-31
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| Keywords | デルサルト理論 / 球面集合 / 正則グラフ / グラフの固有値 / 最適球面コード |
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| Outline of Final Research Achievements |
We would like to obtain progress of optimal spherical codes in this research project. One of major problems of optimal spherical codes is to find a spherical finite set which has maximum minimum-distance between distinct points among the equal-sized spherical sets. The linear programming bound (Delsarte's method) is a powerful tool to obtain a bound for the size of spherical sets for given distances. For regular graphs, we gave the ``dual'' version of the linear programming bound. The spectrum (the eigenvalues of the adjacency matrix) of a regular graph has some dual relationship to the distances on a finite spherical set. We can expect similar results between spherical codes (spherical finite sets) and regular graphs, and developments of both objects from each other.
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| Free Research Field |
代数的組合せ論
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