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…mehr
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.
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.
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.
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