组合数学(英文版第5版)/经典原版书库
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作者(美)布鲁迪
出版社机械工业出版社
ISBN9787111265252
出版时间2021-06
装帧平装
开本32开
定价79元
货号31564970
上书时间2024-06-29
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目录
Preface
1 What Is Combinatorics?
1.1 Example: Perfect Covers of Chessboards
1.2 Example: Magic Squares
1.3 Example: The Four-Color Problem
1.4 Example: The Problem of the 36 OfFicers
1.5 Example: Shortest-Route Problem
1.6 Example: Mutually Overlapping Circles
1.7 Example: The Game of Nim
1.8 Exercises
2 Permutations and Combinations
2.1 Four Basic Counting Principles
2.2 Permutations of Sets
2.3 Combinations (Subsets) of Sets
2.4 Permutations of Multisets
2.5 Combinations of Multisets
2.6 Finite Probability
2.7 Exercises
3 The Pigeonhole Principle
3.1 Pigeonhole Principle: Simple Form
3.2 Pigeonhole Principle: Strong Form
3.3 A Theorem of Ramsey
3.4 Exercises
4 Generating Permutations and Combinations
4.1 Generating Permutations
4.2 Inversions in Permutations
4.3 Generating Combinations
4.4 Generating r-Subsets
4.5 Partial Orders and Equivalence Relations
4.6 Exercises
5 The Binomial Coefficients
5.1 Pascal's Triangle
5.2 The Binomial Theorem
5.3 Unimodality of Binomial Coefficients
5.4 The Multinomial Theorem
5.5 Newton's Binomial Theorem
5.6 More on Partially Ordered Sets
5.7 Exercises
6 The Inclusion-Exclusion Principle and Applications
6.1 The Inclusion-Exclusion Principle
6.2 Combinations with Repetition
6.3 Derangements
6.4 Permutations with Forbidden Positions
6.5 Another Forbidden Position Problem
6.6 M6bius Inversion
6.7 Exercises
7 Recurrence Relations and Generating Functions
7.1 Some Number Sequences
7.2 Generating Functions
7.3 Exponential Generating Functions
7.4 Solving Linear Homogeneous Recurrence Relations
7.5 Nonhomogeneous Recurrence Relations
7.6 A Geometry Example
7.7 Exercises
8 Special Counting Sequences
8.1 Catalan Numbers
8.2 Difference Sequences and Stirling Numbers
8.3 Partition Numbers
8.4 A Geometric Problem
8.5 Lattice Paths and Schr6der Numbers
8.6 Exercises
9 Systems of Distinct Representatives
9.1 General Problem Formulation
9.2 Existence of SDRs
9.3 Stable Marriages
9.4 Exercises
10 Combinatorial .Designs
10.1 Modular Arithmetic
10.2 Block Designs
10.3 Steiner Triple Systems
10.4 Latin Squares
10.5 Exercises
11 Introduction to Graph Theory
11.1 Basic Properties
11.2 Eulerian Trails
11.3 Hamilton Paths and Cycles
11.4 Bipartite Multigraphs
11.5 Trees
11.6 The Shannon Switching Game
11.7 More on Trees
11.8 Exercises
12 More on Graph Theory
12.1 Chromat,ic Number
12.2 Plane and Planar Graphs
12.3 A Five-Color Theorem
12.4 Independence Number and Clique Number
12.5 Matching Number
12.6 Connectivity
12.7 Exercises
13 Digraphs and Networks
13.1 Digraphs
13.2 Networks
13.3 Matchings in Bipartite Graphs Revisited
13.4 Exercises
14 Polya Counting
14.1 Permutation and Symmetry Groups
14.2 Burnside's Theorem
14.3 Polya's Counting Formula
14.4 Exercises
Answers and Hints to Exercises
Bibliography
Index
内容摘要
本书是系统阐述组合数学基础、理论、方法和实例的优秀教材，出版30多年来多次改版，被MIT、哥伦比亚大学、UIUC、威斯康星
大学等众多国外高校采用，对国内外组合数学教学产生
了较大影响，也是相关学科的主要参考文献之一。
本书侧重于组合数学的概念和思想。包括鸽巢原理、计数技术、排列组合、
Polya计数法、二项式系数、容斥原理、生成函数和递推关系以及组合结构（匹配、实验设计、图）等。深入浅出地表达了作者对该领域
全面和深刻的理解。除包含第4版中的内容外，本版又进行了更新，增加了有限概
率、匹配数等内容。此外，各章均包含大量练习题，并在书末给出了参考答案与提示。
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