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The probability method: Successes and limitations. (English) Zbl 0930.05096

This beautiful little paper contains the reflections of Paul Erdős on one area in which he has been a prime mover:
“Probability methods have of course been used a great deal in various branches of analysis and one could write a nice paper about successes and limitations in this field. In this paper I will restrict myself to uses of the probability method in combinatorics and number theory. I worked on various aspects of these problems for nearly 60 years.”
It is delightful reading.

MSC:

05D40 Probabilistic methods in extremal combinatorics, including polynomial methods (combinatorial Nullstellensatz, etc.)
05C15 Coloring of graphs and hypergraphs
05C80 Random graphs (graph-theoretic aspects)
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References:

[1] Bollobás, B., The chromatic number of random graphs, Combinatorica, 8, 49-55 (1988) · Zbl 0666.05033
[2] Erdös, P.; Szekeres, G., A combinatorial problem in geometry, Comportio Math., 2, 463-470 (1935) · Zbl 0012.27010
[3] Spencer, J., Ramsey’s theorem, a new lower bound, J. Combin. Theory Ser. A, 18, 108-115 (1975) · Zbl 0296.05003
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