On the Erdős-Szekeres convex polygon problem
نویسندگان
چکیده
منابع مشابه
On the Erdos-Szekeres convex polygon problem
Let ES(n) be the smallest integer such that any set of ES(n) points in the plane in general position contains n points in convex position. In their seminal 1935 paper, Erdős and Szekeres showed that ES(n) ≤ ( 2n−4 n−2 ) + 1 = 4. In 1960, they showed that ES(n) ≥ 2 + 1 and conjectured this to be optimal. In this paper, we nearly settle the Erdős-Szekeres conjecture by showing that ES(n) = 2.
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Let ES(n) denote the least integer such that among any ES(n) points in general position in the plane there are always n in convex position. In 1935, P. Erdős and G. Szekeres showed that ES(n) exists and ES(n) ≤ ` 2n−4 n−2 ́ + 1. Six decades later, the upper bound was slightly improved by Chung and Graham, a few months later it was further improved by Kleitman and Pachter, and another few months ...
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ژورنال
عنوان ژورنال: Journal of the American Mathematical Society
سال: 2016
ISSN: 0894-0347,1088-6834
DOI: 10.1090/jams/869