A research on symbolic and algebraic computation of groups and combinatorics and its application
| Project/Area Number |
23540011
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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 | University of Yamanashi |
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Principal Investigator |
MIYAMOTO Izumi 山梨大学, 医学工学総合研究部, 教授 (60126654)
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| Project Period (FY) |
2011 – 2013
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| Project Status |
Completed (Fiscal Year 2013)
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| Budget Amount *help |
¥2,600,000 (Direct Cost: ¥2,000,000、Indirect Cost: ¥600,000)
Fiscal Year 2013: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2012: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2011: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
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| Keywords | 代数的数式処理 / アソシエーションスキーム / 置換群 / 数式処理 / 組合せデザイン / スーパースキーム |
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| Research Abstract |
In a previous research I applyed automorphism groups of association schemes to speed up the computation of normalizers of transitive groups. Automorphism groups of coherent configurations are related to the normalizers of permutation groups which may not be transitive. This time, I applied them to speed up the computation of normalizers and testing conjugacy of subgroups of permutation groups which may not be transitive.
Doubly transitive groups form a trivial association scheme same as those formed by symmetric groups. The action of a permutation group on t-tuples of points forms t-superscheme. A t-superscheme consists of partitions of k-tuples of a set of points for k=1, 2,.., t satisfying certain conditions. Doubly transitive groups form 3-superschemes with only one partition on distinct 2-tuples of points. Using computers, we constructed such 3-superschems of moderate size but not formed by doubly transitive groups and, as an application, obtained 2-designs from some of the schemes.
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Report
(4 results)
Research Products
(13 results)
