Structures and Representations of Association Schemes
Structures and Representations of Association Schemes
批准号:
12640039
负责人:
SUZUKI Hiroshi
金额:
$2.05万
依托单位国家:
日本
项目类别:
Grant-in-Aid for Scientific Research (C)
财政年份:
2000
资助国家:
日本
项目状态:
已结题
起止时间:
2000 至 2003
中文摘要
a.代数与几何的联系:定义了关于距离正则图基子集的Terwilliger代数,并对其进行了广泛的研究。该代数的使用使研究任意端点的Terwilliger代数的模变得容易,并给出了Delsarte代数理论与Terwilliger代数及其模之间的联系。平衡条件:分类了q -多项式群关联方案。弱距离正则有向图:给出了弱距离正则有向图的定义和各种构造。部分作为与王开顺的合作,完成了二级案例的分类,以及被称为薄的规则群案例。3度病例和2周围病例进展中。II型矩阵:作为与Rie Hosoya的联合工作,证明了如果II型矩阵是非基元的,它可以分解为较小尺寸的II型矩阵的广义张量积。期望将这一结果应用于非基元自旋模型的分类。距离正则图的绝对界猜想及相关主题:完成并发表了(s, 2)阶距离正则图的分类。特威利格代数的使用被证明是有用的。特别是,如果图形是3-thin,则几何周长以11为界。
英文摘要
a. Connection between Algebra and Geometry: The Terwilliger algebra with respect to a base subset of a distance-regular grasph was defined and studied extensively. The use of this algebra enables to investigate modules of Terwilliger algebras of any endpoint much easily and gives a connection between the theory of Delsarte and Terwilliger algebra and its modules.b. Balanced Conditions: Q-polynomial group association schemes were classified.c. Weakly Distance-Regular Digraphs: The definition of weakly distance-regular digraphs together with various constructions were given. Partly as a joint work with Kaishun Wang, classifications of the case with degree 2, and regular group cases, which are called thin, were completed. Degree 3 cases and girth 2 cases are inprogress.d. Type II Matrices: As a joint work with Rie Hosoya, it was shown that if a type II matrix is imprimitive, it can be decomposed as a generalized tensor product of type II matrices of smaller size. The application of this result to a classification of imprimitive spin models is expected.e. Absolute Bound Conjecture of Distance-Regular Graphs and Related Topics: A classification of distance-regular graphs of order (s, 2) was completed and published. The use of Terwilliger algebra was proved to be useful. In particular, if the graph is 3-thin, geometric girths are bounded by 11.
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H. Suzuki: "Imprimitive Q-polynomial Association Schemes"Journal of Algebraic Combinatorics. 7. 165-180 (1998)
H. Suzuki:“imprimitive Q-多项式关联方案”代数组合学杂志。
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通讯作者:
H. Suzuki: "Association Schemes with Multiple Q-polynomial Structures"Journal of Algebraic Combinatorics. 7. 181-196 (1998)
H. Suzuki:“关联方案与多个 Q 多项式结构”代数组合学杂志。
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M.Kiyota, H.Suzuki: "Character Products and Q-polynomial Group Association Schemes"Journal of Algebra. (to appear).
M.Kiyota,H.Suzuki:“字符积和 Q 多项式群关联方案”代数杂志。
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Rie Hosoya: "Type II Matrices and Their Bose-Mesner Algebras"Journal of Algebraic Combinatorics. 17・1. 19-37 (2003)
Rie Hosoya:“II 型矩阵及其 Bose-Mesner 代数”代数组合学杂志 17・1(2003 年)。
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Kaishun Wang: "Weakly Distance-Regular Digraphs"Discrete Mathematics. 26・1-3. 225-233 (2003)
王凯顺:“弱距离-正则图”离散数学26・1-3(2003)。
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