A Tribute to Paul Erdos
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This volume is dedicated to Paul Erdos, who has profoundly influenced mathematics this century, with over 1200 papers in number theory, complex analysis, probability theory, geometry, interpretation theory, algebra set theory and combinatorics. One of Erdos' hallmarks is the host of stimulating problems and conjectures, to many of which he has 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 v...
This volume is dedicated to Paul Erdos, who has profoundly influenced mathematics this century, with over 1200 papers in number theory, complex analysis, probability theory, geometry, interpretation theory, algebra set theory and combinatorics. One of Erdos' hallmarks is the host of stimulating problems and conjectures, to many of which he has 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.
Table of contents:
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. Multplicative 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.
This volume is dedicated to Paul Erdos, who has profoundly influenced mathematics this century, with over 1200 papers in number theory, complex analysis, probability theory, geometry, interpretation theory, algebra set theory and combinatorics. One of Erdos' hallmarks is the host of stimulating problems and conjectures, to many of which he has 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'!
Table of contents:
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. Multplicative 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.
This volume is dedicated to Paul Erdos, who has profoundly influenced mathematics this century, with over 1200 papers in number theory, complex analysis, probability theory, geometry, interpretation theory, algebra set theory and combinatorics. One of Erdos' hallmarks is the host of stimulating problems and conjectures, to many of which he has 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'!
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