内容简介
组合学是一门关于有限集的计数、存在、构造和优化问题的数学学科。本书着重于前三类问题，内括：基本计数和存在原理、分布、生成函数、递推关系、Pólya理论、组合设计、纠错码、偏序集，以及图论的一些应用括树的计数、色多项式和Ramsey理论入门)。阅读本书只需掌握单变量微积分，并熟悉集合论和基本的证明技巧。 本书着重论述了组合学的特点：双射和组合证明、递归分析和计数问题分类。本书适用范围极广，可用于组合数学的本科课程、离散数学的学期课程、应用数学的研究生入门课程，同时适合自学。本书之所以称为导引，在于分布在全书八章中的大约350个问题。这些问题可用来检查学，也让读者为每节后的练有470多个)做好准备。大部分章节以游记结尾，通过趣闻轶事、未解决问题一步阅读的建议以及与所闻所见有关的数学家传记的形式，为内容增色不少。
目录
PrefaceBefore you go1 Principles of Combinatorics 1.1 Typical counting questions and the product principle 1.2 Counting,overcounting, and the sum principle 1.3 Functions and the bijection principle 1.4 Relations and the equivalence principle 1.5 Existence and the pigeonhole principle2 Distributions and Combinatorial Proofs 2.1 Counting functions 2.2 Counting sets and multisets 2.3 Counting set partitions 2.4 Counting integer partitions3 Algebraic Tools 3.1 Inclusion-exclusion 3.2 Mathematical induction 3.3 Using generating functions, part Ⅰ 3.4 Using generating functions, part Ⅱ 3.5 Techniques for solving recurrence relations 3.6 Solving linear recurrence relations4 Famous Number Families 4.1 Binomial and multinomial coefficients 4.2 Fibonacci and Lucas numbers 4.3 Stirling numbers 4.4 Integer partition numbers5 Counting Under Equivalence 5.1 Two examples 5.2 Permutation groups 5.3 Orbits and fixed point sets 5.4 Using the CFB theorem 5.5 Proving the CFB theorem 5.6 The cycle index and Polya's theorem6 Combinatorics on Graphs 6.1 Basic graph theory 6.2 Counting trees 6.3 Coloring and the chromatic polynomial 6.4 Ramsey theory7 Designs and Codes 7.1 Construction methods for designs 7.2 The incidence matrix and symmetric designs 7.3 Fisher's inequality and Steiner systems 7.4 Perfect binary codes 7.5 Codes from designs, designs from codes8 Partially Ordered Sets 8.1 Poset examples and vocabulary 8.2 Isomorphism and Sperner's theorem 8.3 Dilworth's theorem 8.4 Dimension 8.5 Mobius inversion, part Ⅰ 8.6 Mobius inversion, part ⅡBibliographyHints and Answers to Selected ExercisesList of NotationIndexabout the Author