Claims

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1974_02_01_burr_grunbaum_sloane: Points on a cubic curve give at least 1 + floor(n(n-3)/6) lines through exactly three of n points; with the pair count this makes both limits for k = 3 equal to 1/6.

2012_08_23_green_tao: For all large n, at most floor(n(n-3)/6) + 1 lines contain exactly three of n points in the plane; with the cubic-curve construction this is the exact value of f_3(n).

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