Claims

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1935_01_01_erdos_szekeres: Erdős and Szekeres (Compositio Math. 1935) publish Esther Klein's proof that any five points in the plane, no three collinear, contain four in convex position, so f(4) = 5, the instance n = 4 of the conjecture; refereed.

1960_01_01_erdos_szekeres: Erdős and Szekeres (1960/61) construct, for every n, a set of 2^(n-2) points in the plane with no three collinear and no n in convex position, so f(n) is at least 2^(n-2) + 1, the lower half of the conjecture; refereed.

2006_10_01_szekeres_peters: Szekeres and Peters (ANZIAM J. 2006) prove by computer that every 17 points in the plane with no three collinear contain six in convex position; with the 16-point construction this gives f(6) = 17, the instance n = 6.

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