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Square array T(n,k) (n >= 2, k >= 1) giving smallest positive integer m such that any set of m points in general position in R^n contains k points in convex position, read by antidiagonals.
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%I #3 Mar 30 2012 16:49:04

%S 1,1,2,1,2,3,1,2,3,5,1,2,3,4,9,1,2,3,4,6

%N Square array T(n,k) (n >= 2, k >= 1) giving smallest positive integer m such that any set of m points in general position in R^n contains k points in convex position, read by antidiagonals.

%H W. Morris and V. Soltan, <a href="http://www.ams.org/journal-getitem?pii=S0273-0979-00-00877-6">The Erdos-Szekeres problem on points in convex position - a survey</a>, Bull. Amer. Math. Soc., 37 (No. 4, 2000), 437-458.

%e Array begins:

%e 1 2 3 5 9 ? ...

%e 1 2 3 4 6 9 ...

%e 1 2 3 4 5 7 ...

%K tabl,nonn,nice,hard

%O 0,3

%A _N. J. A. Sloane_, Mar 19 2001