A Tribute to Paul Erdos

A feature of this volume is a collection of some 50 outstanding unsolved problems, together with their 'value'!

A. Baker (Edited by), B. Bollobás (Edited by), A. Hajnal (Edited by)

9780521067331, Cambridge University Press

Paperback / softback, published 26 June 2008

500 pages
23.4 x 15.5 x 2.6 cm, 0.75 kg

This volume is dedicated to Paul Erdos, who profoundly influenced mathematics in the twentieth century, with over 1200 papers in number theory, complex analysis, probability theory, geometry, interpretation theory, algebra set theory and combinatorics. One of Erdos' hallmarks was the host of stimulating problems and conjectures, to many of which he attached monetary prices, in accordance with their notoriety. A feature of this volume is a collection of some 50 outstanding unsolved problems, together with their 'value'! Eminent mathematicians from around the world have contributed articles to this volume that reflect the diversity of Erdos' interests, and it will be a fund of insight for number theorists, combinatorialists, set theorists and analysts.

Frontispiece
List of contributors
Preface
1. Generating expanders from two permutations M. Ajtai, J. Komols and E. Szemeredi
2. Sum-free subsets N. Alon and D. J. Kleitman
3. Is there a different proof of the Erdos-Rado theorem? J. E. Baumgartner
4. Almost collinear triples among N points on the plane J. Beck
5. Hamilton cycles in random graphs of minimal degree at least |k| B. Bollobas, T. I. Fenner and A. M. Frieze
6. The circumference of a graph with a given minimal degree B. Bollobas and R. Haggkvist
7. On arithmetic progressions in sums of sets of integers J. Bourgain
8. Partitions sans petits sommants J. Dixmier and J. L. Nicolas
9. A compact sequential space A. Dow
10. The critical parameter for connectedness of some random graphs R. Durret and H. Kesten
11. Multiplicative functions on arithmetic progressions: the large moduli P. D. T. A. Elliott
12. Locally finite groups of permutations of N acting on loo M. Foreman
13. Hypergraphs games and the chromatic number F. Galvin
14. On arithmetic graphs associated with integral domains K. Gyory
15. On the number of certain subgraphs of graphs without large cliques and independent subsets A. Hajnal, Z. Nagy and L. Soukup
16. Sets of multiples and Behrend sequences R. R. Hall
17. A functional equation arising from the mortality tables W. K. Hayman
18. The differences between consecutives primes, IV R. Heath-Brown
19. On the cofinality of countable products of cardinal numbers T. Jech
On a-centered posets I. Juhasz and K. Kunen
20. A Galvin-Hajnal conjecture on uncountably chromatic graphs P. Komjath
21. Necessary conditions for mean convergence of Hermite-Fejer interpolation A. Mate and P. Nevai
22. Graphs with no unfriendly partitions E. C. Milner and S. Shelah
23. On the Erdos-Fuchs theorem H. L. Montgomery and R. C. Vaughan
24. A tournament which is not finitely representable Z. Nagy and Z. Szentmiklossy
25. On the volume of spheres covered by a random walk P. Revesz
26. Special Lucas sequences, including the Fibonacci sequence, modulo a prime A. Schinzel
27. A remark on heights of subspaces W. Schmidt and S. Shelah
28. On the greatest prime factor of an arithmetical progression T. N. Shorey and R. Tijdeman
29. The probabilistic lens: Sperner, Turan and Bergman revisited J. Spencer
30. On the mean convergence of derivatives of Lagrange interpolation J. Szabodos and A. K. Varma
31. Sur une question d'Erdos et Schinzel G. Tenenbaum
32. Some recent results on interpolation P. Vertesi
33. Partitioning the quadruples of topological spaces W. Weiss
Selected problems.

Subject Areas: Combinatorics & graph theory [PBV]