Synopsis
A Course in Combinatorics 2nd Edition Book Description 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. Contents Preface 1. Graphs 2. Trees 3. Colorings of graphs and Ramsey's theorem 4. Turn'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 Mbius 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: e
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A Course In Combinatorics 2/Ed
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