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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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The category theoretic origin of arithmetic product
The arithmetic product is indeed obtained by Day convolution – it is induced by the product of natural numbers – and is studied as the matrix monoidal structure of Dwyer–Hess's The Boardman-Vogt tenso …