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组合学:导论（影印版）

样章
作者：
David R. Mazur
定价：
169.00元
ISBN：
978-7-04-055633-9
版面字数：
670.000千字
开本：
16开
全书页数：
暂无
装帧形式：
精装
重点项目：
暂无
出版时间：
2021-03-09
读者对象：
学术著作
一级分类：
自然科学
二级分类：
数学与统计
三级分类：
数论
暂无
  • 前辅文
  • 1 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 principle
  • 2 Distributions and Combinatorial Proofs
    • 2.1 Counting functions
    • 2.2 Counting subsets and multisets
    • 2.3 Counting set partitions
    • 2.4 Counting integer partitions
  • 3 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 relations
  • 4 Famous Number Families
    • 4.1 Binomial and multinomial coefficients
    • 4.2 Fibonacci and Lucas numbers
    • 4.3 Stirling numbers
    • 4.4 Integer partition numbers
  • 5 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 Pólya's theorem
  • 6 Combinatorics on Graphs
    • 6.1 Basic graph theory
    • 6.2 Counting trees
    • 6.3 Coloring and the chromatic polynomial
    • 6.4 Ramsey theory
  • 7 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 codes
  • 8 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 Möbius inversion, part I
    • 8.6 Möbius inversion, part II
  • Bibliography
  • Hints and Answers to Selected Exercises
  • List of Notation
  • Index
  • About the Author

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