A Course in Combinatorics
A Course in Combinatorics
R. M. Wilson, California Institute of Technology
£66.00
GBPThis 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.
- Uniquely comprehensive coverage
- Authors are leading experts
- Very pedagogic - carefully explained
Reviews & endorsements
'Both for the professional with a passing interest in combinatorics and for the students for whom it is primarily intended, this is a valuable book.' The Times Higher Education Supplement
'… it will no doubt become a standard choice among the many texts on combinatorics … fascinating … it is highly recommended reading.' Dieter Jungnichel, Zentralblatt MATH
'This well written textbook can be highly recommended to any student of combinatorics and, because of its breadth, has many new things to tell researchers in the field also.' EMS
'This is a fascinating introduction to almost all aspects of combinatorics. Plenty of interesting problems, concrete examples, useful notes and references complement the main text. This book can be highly recommended to everyone interested in combinatorics.' Monatshefe für Mathematik
'… 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
Product details
November 2001Paperback
9780521006019
620 pages
244 × 170 × 33 mm
1.02kg
66 b/w illus.
Available
Table of Contents
- 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.
