Combinatorics and Probability

ISBN-13: 9780521872072 / Angielski / Twarda / 2007 / 660 str.

Graham Brightwell (London School of Economics and Political;Imre Leader (University of Cambridge);Alex Scott (University of Oxford)

Opis

Combinatorics is an area of mathematics involving an impressive breadth of ideas, and it encompasses topics ranging from codes and circuit design to algorithmic complexity and algebraic graph theory. In a highly distinguished career Bela Bollobas has made, and continues to make, many significant contributions to combinatorics, and this volume reflects the wide range of topics on which his work has had a major influence. It arises from a conference organized to mark his 60th birthday and the thirty-one articles contained here are of the highest calibre. That so many excellent mathematicians have contributed is testament to the very high regard in which Bela Bollobas is held. Students and researchers across combinatorics and related fields will find that this volume provides a wealth of insight to the state of the art."

Recenzje

'… this reviewer was very impressed, and even surprised, by the breadth of the articles of the collection. (Of course, the depth is impressive, too, but that is not surprising, given the pedigree of the contributors.)' MAA Reviews

Spis treści

1. Measures of pseudorandomness for finite sequences: minimal values N. Alon, Y. Kohayakawa, C. Mauduit and V. R. Rödl; 2. MaxCut in H-Free graphs Noga Alon, Michael Krivelevich and Benny Sudakov; 3. A tale of three couplings: Poisson–Dirichlet and GEM approximations for random permutations Richard Arratia, A. D. Barbour and Simon Tavaré; 4. Positional games József Beck; 5. Degree distribution of competition-induced preferential attachment graphs N. Berger, C. Borgs, J. T. Chayes, R. M. D'Souza and R. D. Kleinberg; 6. On two conjectures on packing of graphs Béla Bollobás, Alexandr Kostochka and Kittikorn Nakprasit; 7. Approximate counting and quantum computation M. Bordewich, M. Freedman, L. Lovász and D. Welsh; 8. Absence of zeros for the chromatic polynomial on bounded degree graphs Christian Borgs; 9. Duality in infinite graphs Henning Bruhn and Reinhard Diestel; 10. Homomorphism-homogeneous relational structures Peter J. Cameron and Jaroslav Ne∫etril; 11. A spectral Turán theorem Fan Chung; 12. Automorphism groups of metacirculant graphs of order a product of two distinct primes Edward Dobson; 13. On the number of Hamiltonian cycles in a tournament Ehud Friedgut and Jeff Kahn; 14. The game of JumbleG Alan Frieze, Michael Krivelevich, Oleg Pikhurko and Tibor Szabó; 15. 2-Bases of quadruples Zoltán Füredi and Gyula O. H. Katona; 16. On triple systems with independent neighbourhoods Zoltán Füredi, Oleg Pikhurko and Miklós Simonovits; 17. Quasirandomness, counting and regularity for 3-uniform hypergraphs W. T. Gowers; 18. Triangle-free hypergraphs Ervin Gyori; 19. Odd independent transversals are odd Penny Haxell and Tibor Szabó; 20. The first eigenvalue of random graphs Svante Janson; 21. On the number of monochromatic solutions of x + y = z2 Ayman Khalfalah and Endre Szemerédi; 22. Rapid Steiner symmetrization of most of a convex body and the slicing problem B. Klartag and V. Milman; 23. A note on bipartite graphs wthout 2k-cycles Assaf Naor and Jacques Verstraëte; 24. Book Ramsey numbers and quasi-eandomness V. Nikiforov, C. C. Rousseau and R. H. Schelp; 25. Homomorphism and dimension Patrice Ossona de Mendez and Pierre Rosenstiehl; 26. The distance of a permutation from a subgroup of Sn Richard G. E. Pinch; 27. On dimensions of a random solid diagram Boris Pittel; 28. The small giant component in scale-free random graphs Oliver Riordan; 29. A Dirac-type theorem for 3-uniform hypergraphs Vojtech Rödl, Andrzej Rucinski and Endre Szemerédi; 30. On dependency graphs and the lattice gas Alexander D. Scott and Alan D. Sokal; 31. Solving sparse random instances of max cut and max 2-CSP in linear expected time Alexander D. Scott and Gregory B. Sorkin.