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On a Problem of Erdös and Szekeres
Published online by Cambridge University Press: 20 November 2018
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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.
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- Copyright © Canadian Mathematical Society 1961
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