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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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Proving we can minimize the number of crossings by having a planar embedding of $K_{2,2}$ en...

Say that we draw a graph in the following way: we first draw $n$ planar embeddings of $K_{2,2}$ (that is, we first draw $n$ quadrilaterals) such there are no edges which cross. Then for each of the $K …
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