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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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What breaks down in the theory of affine hyperplane arrangments?

It appears to me that there is a substantial amount of combinatorial algebra and geometry supporting the theory of central hyperplane arrangements (See Topics in Hyperplane Arrangements, Aguiar and M …
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