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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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Average number of cycles in a directed regular graph?

A directed random regular graph is a graph where all vertices have exactly $d_{\rm in}$ edges going in and $d_{\rm out}$ going out. If the graph is undirected, i.e. all vertices have degree $d$, then …
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