Synopses & Reviews
Review
'\"The emphasis...is on structural combinatorics, focusing particularly on designs, graphs, and codes. This focus helps the authors convincingly demonstrate the unity of combinatorics, refuting the prejudice that the subject is just a grab bag of tricks....Wide coverage makes A Course in Combinatorics a basic reference; superb exposition makes it a viable, if demanding, textbook; large type, wide margins, and opaque paper make it a pleasure to the eye. Highly recommended.\" D.V. Feldman, Choice\"...their choice of subject matter is superb...would indeed make an excellent text for a full-year introduction to combinatorics.\" George E. Andrews, 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'
Synopsis
This major textbook, a product of many yearsâteaching, will appeal to all teachers of combinatorics who appreciate the breadth and depth of the subject.
Table of Contents
1. Graphs; 2. Trees; 3. Colourings of graphs and Ramseyâs theorem; 4. Turán's theorem; 5. Systems of distinct representatives; 6. Dilworthâs 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 generated 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 geometry; 27. Difference sets and automorphisms; 28. Difference sets and the group ring; 29. Codes and symmetric designs; 30. Association schemes; 31. Algebraic graphs: eigenvalue techniques; 32. Graphs: planarity and duality; 33. Graphs: colourings and embeddings; 34. Trees, electrical networks and squared rectangles; 35. Pólya theory of counting; 36. Baranyaiâs theorem; Appendices.