2012 Fiscal Year Final Research Report
Representations of association schemes and their applications
| Project/Area Number |
23740002
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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 | Tohoku University |
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Principal Investigator |
TANAKA Hajime 東北大学, 大学院・情報科学研究科, 准教授 (50466546)
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| Project Period (FY) |
2011 – 2012
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| Keywords | 光学赤外線天文学 / 観測装置開発 |
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| Research Abstract |
Association schemes are certain special decompositions of complete graphs, and provide a unified framework to experimental designs, error-correcting codes, combinatorial designs, and so on. I worked on developing applications of new tools such as semidefinite programming and the Terwilliger algebra, which is a noncommutative semisimple algebra associated with each vertex of an association scheme. In particular, I obtained (among other results) the so-called Fisher-type inequality for relative t-designs as well as a new intersection theorem in extremal set theory. These results should demonstrate the power of these new tools.
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