Research on characterizations of great antipodal sets as tight designs using representation theory
| Project/Area Number |
16K17604
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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 |
Geometry
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| Research Institution | Kitakyushu National College of Technology |
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Principal Investigator |
Kurihara Hirotake 北九州工業高等専門学校, 生産デザイン工学科, 准教授 (60637099)
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| Project Period (FY) |
2016-04-01 – 2021-03-31
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| Project Status |
Completed (Fiscal Year 2020)
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| Budget Amount *help |
¥3,900,000 (Direct Cost: ¥3,000,000、Indirect Cost: ¥900,000)
Fiscal Year 2019: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2018: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2017: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2016: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
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| Keywords | 大対蹠集合 / 対称R空間 / デザイン / 対蹠集合 / デザイン理論 / 距離正則グラフ / エルミート対称空間 / 符号理論 / 幾何学 / 代数学 / 代数的組合せ論 |
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| Outline of Final Research Achievements |
Great antipodal sets on symmetric spaces are ``good'' finite subset of the spaces. In this research, we studied properties of Great antipodal sets on symmetric R-spaces in terms of combinatorics. In the area of combinatorics, we treat t-designs, which can approximate whole spaces.
In general, for a given a great antipodal set, it is not easy to determine t such that the set is a t-design. In this research, we obtained the relations between special irreducible representations and t such that the great antipodal set is a t-design. Moreover, we also obtained the fact that great antipodal sets have the structures of distance-transitive graphs.
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| Academic Significance and Societal Importance of the Research Achievements |
対称空間の大対蹠集合を組合せ論の立場から研究することは我々の独自の視点であり、そのような研究を創出することは学術的な意義をもつと考える。大対蹠集合の組合せ論的情報から全体の空間の情報を引き出せることがわかったのは大変興味深く、対称空間の研究を組合せ論の言葉で翻訳できることは、今後の数学の発展にも寄与するものと考える。
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Report
(6 results)
Research Products
(31 results)
