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On a Problem of Erdös and Szekeres

Published online by Cambridge University Press:  20 November 2018

F. V. Atkinson
F. V. Atkinson*
Affiliation:
University of Toronto
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where the maximum is over all real θ, and the lower bound is over all sets of positive integers a1 ≤ a2 ≤ … ≤ an. The problem of the order of magnitude of f(n) was posed by Erdös and Szekeres [1], side by side with a number of other interesting questions. Writing g(n) = log f(n), it is obvious that g(n) is sub-additive, in the sense that g(m+n) ≤ g(m) + g(n), and also that g(1) = log 2, so that g(n) ≤ n log 2.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 4 , Issue 1 , January 1961 , pp. 7 - 12
Copyright
Copyright © Canadian Mathematical Society 1961

References

1. Erdös, P. and Szekeres, G., On the product , Acad. Serbe. Sci. Publ. Inst. Math. 13 (1959), 29-34.Google Scholar
2. Cohen, P. J., A conjecture of Littlewood on exponential sums, Report of the Institute in the Theory of Numbers, University of Colorado, Boulder, 1959.Google Scholar