A Structural Theorem for Sets with Few Triangles
Combinatorica - Trang 1-24
Tóm tắt
We show that if a finite point set $$P\subseteq {\mathbb {R}}^2$$ has the fewest congruence classes of triangles possible, up to a constant M, then at least one of the following holds. This provides evidence for two conjectures of Erdős. We use the result of Petridis–Roche–Newton–Rudnev–Warren on the structure of the affine group combined with classical results from additive combinatorics.
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