A comprehensive study of combinatorial objects by algebraic methods
| Project/Area Number |
25400034
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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 |
Algebra
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| Research Institution | Tohoku University |
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Principal Investigator |
TANAKA Hajime 東北大学, 情報科学研究科, 准教授 (50466546)
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| Project Period (FY) |
2013-04-01 – 2017-03-31
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| Project Status |
Completed (Fiscal Year 2016)
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| Budget Amount *help |
¥4,810,000 (Direct Cost: ¥3,700,000、Indirect Cost: ¥1,110,000)
Fiscal Year 2016: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2015: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2014: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2013: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
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| Keywords | アソシエーションスキーム / 距離正則グラフ / Terwilliger 代数 / 半正定値計画 / 直交多項式 / 符号 / 組合せデザイン / 代数的組合せ論 / デザイン / 交叉定理 / 交差定理 |
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| Outline of Final Research Achievements |
I studied, from the viewpoints of both theory and applications, the representation theory of several non-commutative semisimple algebras, such as the Terwilliger algebra attached to each vertex of an association scheme, which is a certain special decomposition of a complete graph. I obtained various results related to extremal set theory, design theory, coding theory, etc., where the representation theory is applied together with the duality of semidefinite programming as well as systems of orthogonal polynomials associated with irreducible modules of these algebras. I have been involved with the recent development of the new tools, and this project contributed to further deepening and strengthening of them.
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Report
(5 results)
Research Products
(25 results)
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[Journal Article] Distance-regular graphs2016
Author(s)
Edwin R. van Dam, Jack H. Koolen, Hajime Tanaka
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Journal Title
The Electronic Journal of Combinatorics
Volume: －
Related Report
Peer Reviewed / Open Access / Int'l Joint Research / Acknowledgement Compliant
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[Journal Article] Arithmetic completely regular codes2016
Author(s)
Jack H. Koolen, Woo Sun Lee, William J. Martin, Hajime Tanaka
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Journal Title
Discrete Mathematics & Theoretical Computer Science
Volume: 17
Pages: 59-76
Related Report
Peer Reviewed / Open Access / Int'l Joint Research / Acknowledgement Compliant
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