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A course in combinatorics / J.H. van Lint and R.M. Wilson

Author
Lint, Jacobus Hendricus van, 1932-
Published
Cambridge : Cambridge University Press, 2001.
Edition
Second edition.
Physical Description
1 online resource (xiv, 602 pages) : digital, PDF file(s).
Additional Creators
Wilson, R. M. (Richard Michael), 1945-
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Contents
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.
Summary
This is the second edition of a popular book on combinatorics, a subject dealing with ways of arranging and distributing objects, and which 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 essential for workers in many scientific fields to have some familiarity with the subject. The authors have tried to be as comprehensive as possible, dealing in a unified manner with, for example, 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. The book is ideal for courses on combinatorical mathematics at the advanced undergraduate or beginning graduate level. Working mathematicians and scientists will also find it a valuable introduction and reference.
Subject(s)
ISBN
9780511987045 (ebook)
9780521803403 (hardback)
9780521006019 (paperback)
Note
Title from publisher's bibliographic system (viewed on 18 Jul 2016).
View MARC record | catkey: 34830440