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A course in combinatorics /
| Autor principal: | |
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| Otros Autores: | |
| Formato: | Libro |
| Lenguaje: | English |
| Publicado: |
Cambridge, U.K. ; New York :
Cambridge University Press,
2001.
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| Edición: | Second edition |
| Materias: | |
| Acceso en línea: | Sample text Publisher description Table of contents |
Tabla de Contenidos:
- 1. Graphs 1
- 2. Trees 12
- 3. Colorings of graphs and Ramsey's theorem 24
- 4. Turan's theorem and extremal graphs 37
- 5. Systems of distinct representatives 43
- 6. Dilworth's theorem and extremal set theory 53
- 7. Flows in networks 61
- 8. De Bruijn sequences 71
- 9. Two (0, 1 *) problems: addressing for graphs and a hash-coding scheme 77
- 10. The principle of inclusion and exclusion; inversion formulae 89
- 11. Permanents 98
- 12. The Van der Waerden conjecture 110
- 13. Elementary counting; Stirling numbers 119
- 14. Recursions and generating functions 129
- 15. Partitions 152
- 16. (0, 1)-Matrices 169
- 17. Latin squares 182
- 18. Hadamard matrices, Reed--Muller codes 199
- 19. Designs 215
- 20. Codes and designs 244
- 21. Strongly regular graphs and partial geometries 261
- 22. Orthogonal Latin squares 283
- 23. Projective and combinatorial geometries 303
- 24. Gaussian numbers and q-analogues 325
- 25. Lattices and Mobius inversion 333
- 26. Combinatorial designs and projective geometries 351
- 27. Difference sets and automorphisms 369
- 28. Difference sets and the group ring 383
- 29. Codes and symmetric designs 396
- 30. Association schemes 405
- 31. (More) algebraic techniques in graph theory 432
- 32. Graph connectivity 451
- 33. Planarity and coloring 459
- 34. Whitney Duality 472
- 35. Embeddings of graphs on surfaces 491
- 36. Electrical networks and squared squares 507
- 37. Polya theory of counting 522
- 38. Baranyai's theorem 536
- Appendix 1. Hints and comments on problems 542
- Appendix 2. Formal power series 578.