A Course in Combinatorics

ISBN-13: 9780521006019 / Angielski / Miękka / 2001 / 620 str.

J. H. Van Lint; R. M. Wilson

Opis

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.

Recenzje

'… 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

Spis treści

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.