Abstract
Just as we started this book with the first papers of Paul Erdős in number theory, we close it by discussing what will possibly be considered his most lasting legacy — the introduction, together with Alfred Rényi, of the probabilistic method. Stated in the simplest way it says:
If, in a given set of objects, the probability that an object does not have a certain property is less than 1, then there must exist an object with this property.
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References
M. Ajtai, V. Chvátal, M. Newborn & E. Szemerédi: Crossing-free subgraphs, Annals of Discrete Math. 12 (1982), 9–12.
N. Alon & J. Spencer: The Probabilistic Method, Second edition, Wiley-Interscience 2000.
P. Erdős: Some remarks on the theory of graphs, Bulletin Amer. Math. Soc. 53 (1947), 292–294.
P. Erdős: Graph theory and probability, Canadian J. Math. 11 (1959), 34–38.
P. Erdős: On a combinatorial problem I, Nordisk Math. Tidskrift 11 (1963), 5–10.
P. Erdős & R. K. Guy: Crossing number problems, Amer. Math. Monthly 80 (1973), 52–58.
P. Erdős & A. RÉnyt: On the evolution of random graphs, Magyar Tud. Akad. Mat. Kut. Int. Kozl. 5 (1960), 17–61.
T. Leighton: Complexity Issues in Vlsi, MIT Press, Cambridge MA 1983.
L. A. Székely: Crossing numbers and hard Erdos problems in discrete geometry, Combinatorics, Probability, and Computing 6 (1997), 353–358.
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© 2001 Springer-Verlag Berlin Heidelberg
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Aigner, M., Ziegler, G.M. (2001). Probability makes counting (sometimes) easy. In: Proofs from THE BOOK. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-04315-8_32
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DOI: https://doi.org/10.1007/978-3-662-04315-8_32
Publisher Name: Springer, Berlin, Heidelberg
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