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Abstract incidence geometries like projective spaces, polar spaces, generalized polygons, as well as incidence problems in the real or complex Euclidean spaces (eg. Szemerédi–Trotter theorem).
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Points on $k$ Circles
Let $k$ be a fixed positive integer. We want to find the minimum number $f(k)$, such that for a set of finite points in the plane, if any $f(k)$ of them are on $k$ circles, then all of them are on $k$ …