A Course in Combinatorics

Second edition of a popular text which covers the whole field of combinatorics.

J. H. van Lint (Author), R. M. Wilson (Author)

9780521006019, Cambridge University Press

Paperback, published 22 November 2001

620 pages, 66 b/w illus.
24.4 x 17 x 3.3 cm, 1.02 kg

'… becoming a modern classic … every good student should progress to this book at some stage: it is a wonderful source of elegant proofs and tantalising examples. No-one will find it easy, but every budding or established combinatorialist will be enriched by it … This text is unashamedly and impressively mathematical; it will challenge and inform every reader and is a very significant achievement.' The Mathematical Gazette

This is the second edition of a popular book on combinatorics, a subject dealing with ways of arranging and distributing objects, and which involves ideas from geometry, algebra and analysis. The breadth of the theory is matched by that of its applications, which include topics as diverse as codes, circuit design and algorithm complexity. It has thus become essential for workers in many scientific fields to have some familiarity with the subject. The authors have tried to be as comprehensive as possible, dealing in a unified manner with, for example, graph theory, extremal problems, designs, colorings and codes. The depth and breadth of the coverage make the book a unique guide to the whole of the subject. The book is ideal for courses on combinatorical mathematics at the advanced undergraduate or beginning graduate level. Working mathematicians and scientists will also find it a valuable introduction and reference.

Preface
1. Graphs
2. Trees
3. Colorings of graphs and Ramsey's theorem
4. Turán's theorem and extremal graphs
5. Systems of distinct representatives
6. Dilworth's theorem and extremal set theory
7. Flows in networks
8. De Bruijn sequences
9. The addressing problem for graphs
10. The principle of inclusion and exclusion: inversion formulae
11. Permanents
12. The Van der Waerden conjecture
13. Elementary counting: Stirling numbers
14. Recursions and generating functions
15. Partitions
16. (0,1)-matrices
17. Latin squares
18. Hadamard matrices, Reed-Muller codes
19. Designs
20. Codes and designs
21. Strongly regular graphs and partial geometries
22. Orthogonal Latin squares
23. Projective and combinatorial geometries
24. Gaussian numbers and q-analogues
25. Lattices and Möbius inversion
26. Combinatorial designs and projective geometries
27. Difference sets and automorphisms
28. Difference sets and the group ring
29. Codes and symmetric designs
30. Association schemes
31. Algebraic graph theory: eigenvalue techniques
32. Graphs: planarity and duality
33. Graphs: colorings and embeddings
34. Electrical networks and squared squares
35. Pólya theory of counting
36. Baranyai's theorem
Appendices
Name index
Subject index.

Subject Areas: Combinatorics & graph theory [PBV]