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On a problem of P. Erdős

Part of: Combinatorics

Published online by Cambridge University Press:  26 February 2010

E. Szemerédi
E. Szemerédi
Affiliation:
Matematikai Kutató Intezele, Budapest, Hungary.
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Extract

The letters a, b, n, m, t (perhaps with suffixes) always denote natural numbers. A, B, S denote finite sets of natural numbers. |A| stands for the cardinality of A.

For a given constant c > 1 we say that the set A has property α(c) if there are at most c|A| differences a − b ≥ 0 for a, b ∈ A.

MSC classification

Secondary: 05A99: None of the above, but in this section
Type
Research Article
Information
Mathematika , Volume 20 , Issue 2 , December 1973 , pp. 226 - 228
Copyright
Copyright © University College London 1973

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References

1. Roth, K. F., “On certain sets of integers”, J. London Math. Soc., 28 (1953), 104–109.CrossRefGoogle Scholar
2. Szemerédi, E., “On sets of integers containing no four elements in arithmetic progression”, Acta Math. Acad. Sci. Hung., 20 (1969), 89–104.CrossRefGoogle Scholar