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A Course in Combinatorics
Taschenbuch von R. M. Wilson
Sprache: Englisch

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Beschreibung
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.
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.
Inhaltsverzeichnis
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.
Details
Erscheinungsjahr: 2009
Genre: Mathematik
Rubrik: Naturwissenschaften & Technik
Medium: Taschenbuch
Seiten: 620
ISBN-13: 9780521006019
ISBN-10: 0521006015
Sprache: Englisch
Ausstattung / Beilage: Paperback
Einband: Kartoniert / Broschiert
Autor: Wilson, R. M.
Auflage: 2. Auflage
Hersteller: Cambridge University Press
Maße: 244 x 170 x 34 mm
Von/Mit: R. M. Wilson
Erscheinungsdatum: 30.03.2009
Gewicht: 1,054 kg
preigu-id: 102551867
Inhaltsverzeichnis
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.
Details
Erscheinungsjahr: 2009
Genre: Mathematik
Rubrik: Naturwissenschaften & Technik
Medium: Taschenbuch
Seiten: 620
ISBN-13: 9780521006019
ISBN-10: 0521006015
Sprache: Englisch
Ausstattung / Beilage: Paperback
Einband: Kartoniert / Broschiert
Autor: Wilson, R. M.
Auflage: 2. Auflage
Hersteller: Cambridge University Press
Maße: 244 x 170 x 34 mm
Von/Mit: R. M. Wilson
Erscheinungsdatum: 30.03.2009
Gewicht: 1,054 kg
preigu-id: 102551867
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