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Enumerative combinatorics, graph theory, order theory, posets, matroids, designs and other discrete structures. It also includes algebraic, analytic and probabilistic combinatorics.
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Does a certain points and lines configuration exist?
Using a Pappian-ish configuration, we can get $n = 5$ and $n = 7$.
For $n = 7$, put points at $(x,0)$ and $(x,1)$ for integer $x$ with $0 \le x \le 3$, at $(x,1/2)$ for integer or half-integer $x$ wi …