组合数学:专题、技术与算法(英文版)
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图灵原版数学统计学系列

组合数学:专题、技术与算法(英文版)

终止销售
这本优秀的组合数学教材是作者20多年研究和教学经验的结晶.全书分成初级篇和高级篇两个部分,共18章内容,每章都以“专题-技术-算法”的模式呈现,阐述深入浅出,简明易懂.本书几乎涵盖了组合数学中所有有趣的主题,如中国邮递员问题、中国的九连环问题、友谊定理等,当然也收集了若干前沿内容.
本书适合作为高等院校高年级本科生与低年级研究生的组合数学课程教材,也适合各理工学科科研人员参考.
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出版信息

  • 书  名组合数学:专题、技术与算法(英文版)
  • 系列书名图灵原版数学统计学系列
  • 执行编辑关于本书的内容有任何问题,请联系 傅志红
  • 出版日期2009-07-20
  • 书  号978-7-115-21087-6
  • 定  价59.00 元
  • 页  数364
  • 开  本16开
  • 出版状态终止销售
  • 原书名Combinatorics: Topics, Techniques, Algorithms
  • 原书号0-521-45761-0

同系列书

目录

1. What is Combinatorics? 1
Sample problems How to use this book What you need to know Exercises
2. On numbers and counting 7
Natural numbers and arithmetic Induction Some useful functions Orders
of magnitude Different ways of counting Double counting Appendix on
set notation Exercises
3. Subsets, partitions, permutations 21
Subsets Subsets of fixed size -- The Binomial Theorem and Pascal's Triangle
-- Project: Congruences of binomial coefficients Permutations Estimates for
factorials, Selections Equivalence and order Project: Finite topologies
Project: Cayley's Theorem on trees Bell numbers Generating combinatorial
objects Exercises
4. Recurrence relations and generating functions 49
Fibonacci numbers Aside on formal power series -- Linear recurrence relations
with constant coefficients Derangements and involutions Catalan and Bell
numbers -- Computing solutions to recurrence relations Project: Finite fields
and QUICKSORT Exercises
5. The Principle of Inclusion and Exclusion 75
PIE -- A generalisation Stirling numbers Project: Stirling numbers and
exponentias -- Even and odd permutations Exercises
6. Latin squares and S DRs 87
Latin squares Systems of distinct representatives How many Latin squares ?
Quasigroups -- Project: Quasigroups and groups Orthogonal Latin squares
Exercises
7. Extremal set theory 99
Intersecting families -- Sperner families The De Bruijn-Erdos Theorem
Project: Regular families -- Exercises
8. Steiner triple systems 107
Steiner systems A direct construction A recursive construction -- Packing and
covering Project: Some special Steiner triple systems Project: Tournaments
and Kirkman's schoolgirls Exercises
9. Finite geometry 123
Linear algebra over finite fields Gaussian coefficients -- Projective geometry
Axioms for projective geometry Projective planes Other kinds of geometry
-- Project: Coordinates and configurations Project: Proof of the Bruck-Ryser
Theorem -- Appendix: Finite fields Exercises
10. Ramsey's Theorem 147
The Pigeonhole Principle --- Some special cases Ramsey's Theorem , Bounds
for Ramsey numbers -- Applications The infinite version Exercises

11. Graphs 159
Definitions --- Trees and forests -- Minimal spanning trees -- Eulerian graphs
Hamiltonian graphs -- Project: Gray codes -- The Travelling Salesman
Digraphs --- Networks Menger, KJnig and Hall Diameter and girth
Project: Moore graphs Exercises
12. Posets, lattices and matroids 187
Posers and lattices Linear extensions of a poser Distributive lattices
Aside on propositional logic Chains and antichains Products and dimension
The MJbius function of a poset Matroids Project: Arrow's Theorem
Exercises
13. More on partitions and permutations 209
Partitions, diagrams and conjugacy classes guler's Pentagonal Numbers
Theorem Project: Jacobi's Identity--- Tableaux: Symmetric polynomials
Exercises
14. Automorphism groups and permutation groups 225
Three definitions of a group Examples of groups Orbits and transitivity
The Schreier-Sims algorithm -Primitivity and multiple transitivity Examples
Project: Cayley digraphs and Frucht's Theorem Exercises
15. Enumeration under group action 245
The Orbit-counting Lemma -- An application Cycle index Examples
Direct and wreath products --- Stirling numbers revisited Project: Cycle index
and symmetric functions -- Exercises
16. Designs 257
Definitions and examples To repeat or not to repeat Fisher's Inequality
Designs from finite geometry Small designs Project: Hadamard matrices
Exercises
17. Error-correcting codes 271
Finding out a liar -- Definitions Probabilistic considerations Some bounds
Linear codes; Hamming codes Perfect codes Linear codes and projective
spaces Exercises
18. Graph colourings 291
More on bipartite graphs Vertex colourings -- Project: Brooks' Theorem
Perfect graphs Edge colourings Topological graph theory Project: The
Five-colour Theorem Exercises
19. The infinite 307
Counting infinite sets K~nig's Infinity Lemma Posers and Zorn's Lemma
Ramsey theory -- Systems of distinct representatives Free constructions The
random graph -- Exercises
20. Where to from here? 325
Computational complexity Some graph-theoretic topics Computer software
-- Unsolved problems -- Further reading
Answers to selected exercises 339
Bibliography 343
Index 347
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