Geodesic
On a Problem of Erdös and Szekeres
Canadian mathematical bulletin, Tome 4 (1961) no. 1, pp. 7-12

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Write 1 2 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. 
Atkinson, F. V. On a Problem of Erdös and Szekeres. Canadian mathematical bulletin, Tome 4 (1961) no. 1, pp. 7-12. doi: 10.4153/CMB-1961-002-5
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     title = {On a {Problem} of {Erd\"os} and {Szekeres}},
     journal = {Canadian mathematical bulletin},
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