Combinatorial Matrix Classes组合矩阵组
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作者： Richard A. Brualdi 著
出 版 社：
出版时间： 2006-8-1字数：版次： 1页数： 544印刷时间： 2006/08/01开本： 16开印次： 1纸张： 胶版纸I S B N ： 9780521865654包装： 精装编辑推荐
作者简介
Richard A. Brualdi is UWF Beckwith Bascom Professor of Mathematics at the University of Wisconsin, Madison.
内容简介
Here Steven Finch provides 136 essays, each devoted to a mathematical constant or a class of constants, from the well known to the highly exotic. This book will be helpful both to readers seeking information about a specific constant, and to readers who desire a panoramic view of all constants coming from a particular field, for example combinatorial enumeration or geometric optimization. Unsolved problems appear virtually everywhere as well. This is an outstanding scholarly attempt to bring together all significant mathematical constants in one place.
目录
Preface
Introduction
1.1 Fundamental Concepts
1.2 Combinatorial Parameters
1.3 Square Matrices
1.4 An Existence Theorem
1.5 An Existence Theorem for Symmetric Matrices
1.6 Majorization
1.7 Doubly Stochastic Matrices and Majorization References
2 Basic Existence Theorems for Matrices with Prescribed Properties
2.1 The Gale Ryser and Ford Fulkerson Theorems
2.2 Tournament Matrices and Landau's Theorem
2.3 Symmetric Matrices References
3 The Class A（R, S） of （0,1）-Matrices
3.1 A Special Matrix in A（R,S）
3.2 Interchanges
3.3 The Structure Matrix T（R,S）
3.4 Invariant Sets
3.5 Term Rank
3.6 Widths and Multiplicities
3.7 Trace
3.8 Chromatic Number
3.9 Discrepancy
3.10 Rank
3.11 Permanent
3.12 Determinant
References
4 More on the Class A（R,S） of （0,1）-Matrices
4.1 Cardinality of A（R, S） and the RSK Correspondence
4.2 Irreducible Matrices in A（R,S）
4.3 Fully Indecomposable Matrices in A（R, S）
4.4 A（R, S） and Z+（R, S） with Restricted Positions
4.5 The Bruhat Order on A（R,S）
4.6 The Integral Lattice L（R,S）
4.7 Appendix
References
5 The Class T（R） of Tournament Matrices
5.1 Algorithm for a Matrix in "T（R）
5.2 Basic Properties of Tournament Matrices
5.3 Landau's Inequalities
5.4 A Special Matrix in T（R）
5.5 Interchanges
5.6 Upsets in Tournaments
5.7 Extreme Values of v（R） and/）（R）
5.8 Cardinality of T（R）
5.9 The Class T（R;2） of 2-Tournament Matrices
5.10 The Class A（R,*）o of （0, 1）-Matrices References
6 Interchange Graphs
6.1 Diameter of Interchange Graphs G（R,S）
6.2 Connectivity of Interchange Graphs
6.3 Other Properties of Interchange Graphs
6.4 The A-Interchange Graph GA（R）
6.5 Random Generation of Matrices in A（R,S） and 7-（R）
References
7 Classes of Symmetric Integral Matrices
7.1 Symmetric Interchanges
7.2 Algorithms for Symmetric Matrices
7.3 The Class A（R）o
7.4 The Class A（R）
References
8 Convex Polytopes of Matrices
8.1 Transportation Polytopes
8.2 Symmetric Transportation Polytopes
8.3 Term Rank and Permanent
8.4 Faces of Transportation Polytopes
References
……
9 Doubly Stochastic Matrices
Master SBibliography
Index
