Erdös CentennialLászló Lovász, Imre Ruzsa, Vera T. Sós Springer Science & Business Media, 24 de gen. 2014 - 720 pŕgines Paul Erdös was one of the most influential mathematicians of the twentieth century, whose work in number theory, combinatorics, set theory, analysis, and other branches of mathematics has determined the development of large areas of these fields. In 1999, a conference was organized to survey his work, his contributions to mathematics, and the far-reaching impact of his work on many branches of mathematics. On the 100th anniversary of his birth, this volume undertakes the almost impossible task to describe the ways in which problems raised by him and topics initiated by him (indeed, whole branches of mathematics) continue to flourish. Written by outstanding researchers in these areas, these papers include extensive surveys of classical results as well as of new developments. |
Continguts
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The Phase Transition in the ErdősRényi Random Graph Process | 59 |
Around the Sumproduct Phenomenon | 111 |
Small Doubling in Groups | 129 |
Erdős and Multiplicative Number Theory | 152 |
The History of Degenerate Bipartite Extremal Graph Problems | 169 |
L2 Majorant Principles | 377 |
A Combinatorial Classic Sparse Graphs with High Chromatic Number | 383 |
Small Ball Probability Inverse Theorems and Applications | 408 |
The Beginnings of Geometric Graph Theory | 465 |
Paul Erdős and the Difference of Primes | 485 |
Paul Erdős and the Rise of Statistical Thinking in Elementary Number Theory | 514 |
Extremal Results in Random Graphs | 535 |
Erdőss Work on the Sum of Divisors Function and on Eulers Function | 584 |
Erdős and Arithmetic Progressions | 265 |
Paul Erdős and Egyptian Fractions | 289 |
Perfect Powers in Products with Consecutive Terms from Arithmetic Progressions II | 310 |
Erdőss Work on Infinite Graphs | 325 |
The Impact of Paul Erdős on Set Theory | 347 |
Some Problems and Ideas of Erdős in Analysis and Geometry | 364 |
Some Results and Problems in the Theory of Word Maps | 611 |
Some of Erdős Unconventional Problems in Number Theory Thirtyfour Years Later | 651 |
Erdős on Polynomials | 682 |
Problems Results New Developments | 711 |
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algebraic Algorithms Amer applications arithmetic progressions asymptotic bipartite graph Bollobás Bolyai cardinality chromatic number coloring combinatorial complete graph Comput conjecture conjugacy class constant construction contains cycles defined denote dense graphs density Discrete distribution divisors Egyptian fractions equation Erd˝os Erd˝os’s Erdós ex(n example exists extremal graph extremal problems finite simple groups function Füredi geometry giant component girth graph G graph theory Hajnal hypergraph implies infinite integers János Bolyai k-core least log2 logn Lovász lower bound Luczak Mathematics matrix method number of edges number theory obtained paper partition Paul Erd˝os polynomials positive integers probabilistic probability Proc proof of Theorem proved question Ramsey Ramsey theory random graphs regularity lemma result Rödl satisfies Section sequence Simonovits structure subgraphs subgroup subset Szemerédi triangle-free graphs Turán upper bound values vertex vertices zeros