A course in combinatorics
著者
書誌事項
A course in combinatorics
Cambridge University Press, c1992
- : hbk
- : pbk
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注記
Includes bibliographical references and indexes
内容説明・目次
内容説明
This major textbook, a product of many years' teaching, will appeal to all teachers of combinatorics who appreciate the breadth and depth of the subject. The authors exploit the fact that combinatorics requires comparatively little technical background to provide not only a standard introduction but also a view of some contemporary problems. All of the 36 chapters are in bite-size portions; they cover a given topic in reasonable depth and are supplemented by exercises, some with solutions, and references. To avoid an ad hoc appearance, the authors have concentrated on the central themes of designs, graphs and codes.
目次
- 1. Graphs
- 2. Trees
- 3. Colourings of graphs and Ramsey's theorem
- 4. Turan's theorem
- 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 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 Moebius 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. Polya theory of counting
- 36. Baranyai's theorem
- Appendices.
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