2019 Fiscal Year Final Research Report
Construction of the Delsarte theory for quotient sets
| Project/Area Number |
16K17569
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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 | Aichi University of Education |
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Principal Investigator |
Nozaki Hiroshi 愛知教育大学, 教育学部, 准教授 (80632778)
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| Project Period (FY) |
2016-04-01 – 2020-03-31
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| Keywords | グラフの固有値 / ハイパーグラフ / 線形計画限界 / Delsarte理論 / アソシエーションスキーム / 距離正則グラフ / スペクトラルギャップ |
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| Outline of Final Research Achievements |
The eigenvalues of the adjacency matrix of a graph is called the eigenvalues of the graph. The difference of the degree and the second-largest eigenvalue of a regular graph is called the spectral gap, and the graph which has a large spectral gap has high connectivity in some sense. There are some methods to obtain an upper bound on the number of vertices, so called linear programming bounds. In this research project, we proved the analogous theory of the method for regular bipartite graphs, and extended the theory for regular uniform hypergraphs. Using the linear programming method for regular uniform hypergraphs, we improved and generalized some known results.
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| Free Research Field |
代数的組合せ論
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| Academic Significance and Societal Importance of the Research Achievements |
Delsarte理論とは，アソシエーションスキームまたはランク1対称空間の部分集合に対して，種々の組合せ論的対象に統一的な枠組みを与える理論である．正則一様なハイパーグラフに対する線形計画限界は，Delsarte理論の商集合版にあたり，組合せデザインを初めとする，ある種の正則性を持つ組合せ論的対象に応用可能な理論である．正則一様なハイパーグラフに対する線形計画限界を用いて，アソシエーションスキームの枠組みを超えた，スペクトル理論への応用が期待できる．
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