A density version of a geometric ramsey theorem |
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| Authors: | TC Brown JP Buhler |
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| Institution: | Simon Fraser University, Burnaby, British Columbia V5A 1S6, Canada;Pennsylvania State University, University Park, Pennsylvania 16802 USA |
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| Abstract: | Let V be an n-dimensional affine space over the field with pd elements, p ≠ 2. Then for every ε > 0 there is an n(ε) such that if n = dim(V) ? n(ε) then any subset of V with more than ε|V| elements must contain 3 collinear points (i.e., 3 points lying in a one-dimensional affine subspace). |
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