矩阵结合方案 内容简介

本书论述有限域上各类典型矩阵在群作用下构作的结合方案，其内容主要包括有限域上的长方矩阵、交错矩阵、hermite矩阵、对称矩阵和二次型构作的结合方案，导出各类结合方案的一般参数计算公式，讨论这些结合方案的本原性、对偶性、p多项式等基本性质以及自同构群。书中还特别论述了特征数为2时二次型结合方案的特征值及其聚合方案的对偶方案。该书可供各大专院校作为教材使用，也可供从事相关工作的人员作为参考用书使用。

矩阵结合方案 目录

note from the translator
preface
foreword to the chinese edition
list of symbols
chapter 1 basic theory of association schemes
1.1 definition of association scheme
1.2 examples
1.3 the eigenvalues of association schemes
1.4 the krein parameters
1.5 s-rings and duality
1.6 primitivity and imprimitivity
1.7 subschemes and quotient schemes
1.8 the polynomial property
1.9 the automorphisms
chapter 2 association schemes of rectangular matrices
2.1 definition and primitivity
2.2 the polynomial property of association schemes of rectangular matrices.
2.3 recurrence formulas for intersection numbers
2.4 the duality of association schemes of rectangular matrices
2.5 the automorphisms ofmat(m × n,q)
chapter 3 association schemes of alternate matrices
3.1 primitivity and p-polynomial property
3.2 the parameters of г(1)
3.3 recurrences for intersection numbers
3.4 recurrences for intersection numbers: continued
3.5 the self-duality of alt(n,q)
3.6 the automorphisms of alt(n,q)
chapter 4 association schemes of hermitian matrices
4.1 primitivity and p-polynomial property
4.2 the parameters of graph г(1)
4.3 recurrences for intersection numbers
4.4 recurrences for intersection numbers: continued
4.5 the self-duality of her(n,q2)
4.6 the automorphisms of her(n,q2)
chapter 5 association schemes of symmetric matrices in odd characteristic
5.1 the normal forms of symmetric matrices
5.2 the association schemes of symmetric matrices and their primitivity
5.3 sym(n,q) for small n
5.4 a few enumeration formulas from orthogonal geometry
5.5 calculation of intersection numbers
5.6 calculation of intersection numbers: continued
5.7 the association scheme quad(n,q)
5.8 the self-duality of sym(n,q)
5.9 the automorphisms of sym(n,q)
chapter 6 association schemes of symmetric matrices in even characteristic
6.1 the normal forms of symmetric matrices
6.2 the imprimitivity of sym(n,q)
6.3 the association scheme sym(2,q)
6.4 some results of pseudo-symplectic geometry
6.5 calculation of intersection numbers
6.6 calculation of intersection numbers: continued
6.7 a fusion scheme of sym(n,q)
6.8 the automorphisms of sym(n,q)
chapter 7 association schemes of quadratic forms in even characteristic--.
7.1 the normal forms of quadratic forms
7.2 qua(2,q) and qua(3,q)
7.3 some enumeration formulas from orthogonal geometry
7.4 calculation of intersection numbers
7.5 the duality of association schemes of quadratic forms
7.6 the imprimitivity of association schemes of quadratic forms
7.7 two fusion schemes of qua(n,q)
7.8 the automorphisms of association schemes of quadratic forms
chapter 8 the eigenvalues of association schemes of quadratic forms
8.1 the eigenvalues of association scheme qua(2,q)
8.2 some lemmas on additive characters
8.3 the 1-extensions and fr(n)
8.4 values of fr(n) on the union classes c2i(n)
8.5 the 2-extensions and f2k*(n)
8.6 values of f2k*(n) on classes c2i(n) and c2i(n)∪c2i-1(n)
8.7 dual schemes of two fusion schemes of qua(n,q)
8.8 eigenvalues of small association schemes of quadratic forms
references
index

矩阵结合方案 节选

《矩阵结合方案(英文版)》内容简介：This title is the first in a series of mathematics texts and monographs co-published byScience Press, China and Jones & Bartlett Learning of Sudbury, Massachusetts. Theprimary goal of this partnership is to bring Chinese mathematical research findings to theglobal, English-speaking mathematics community. Each title in this series is put through acareful translation process to promote accuracy. Association Schemes of Matrices is an 8-chapter monograph that has met with widesuccess throughout the Chinese mathematics community. The'main emphasis of this bookis on the association schemes of various types of matrices. The matrix method here iselementary and requires little mathematical background. An undergraduate student who hascompleted a course in linear algebra and abstract algebra will be able to take on a researchproject on matrix groups and their geometries with the matrix techniques that are presentedby the mathematicians that have contributed to this project. The matrix method has provento be effective when the underlying field has fewer elements or in lower dimensions.

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自然科学 数学 代数数论组合理论

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