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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| Project Status |
Completed (Fiscal Year 2012)
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| Budget Amount *help |
¥2,860,000 (Direct Cost: ¥2,200,000、Indirect Cost: ¥660,000)
Fiscal Year 2012: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2011: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000)
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| Keywords | 光学赤外線天文学 / 観測装置開発 / アソシエーションスキーム / 距離正則グラフ / Terwilliger 代数 / デザイン理論 / 半正定値計画法 / Terwilliger代数 / 直交多項式 |
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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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Report
(3 results)
Research Products
(21 results)
