"...their choice of subject matter is superb...would indeed make an excellent text for a full-year introduction
to combinatorics."
--Mathematical Reviews
"...this is a valuable book both for the professional with a passing interest in combinatorics and for the
students for whom it is primarily intended."
--Times Higher Education Supplement
Submitted by Cambridge University Press Web Site, December, 2001
Summary
Combinatorics, a subject dealing with ways of arranging and distributing objects, 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 an essential tool in many scientific
fields. In this second edition the authors have made the text as comprehensive as possible, dealing in a unified
manner with such topics as 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. It is ideal for courses on combinatorical
mathematics at the advanced undergraduate or beginning graduate level, and working mathematicians and scientists
will also find it a valuable introduction and reference.
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
