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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 is the n-th power of the adjacency matrix equal to?

I would need to know what exactly is the definition you are using for a "path" and not a "walk", based on which this answer may be either useful or useless. But the $n^{th}$ power of the adjacency mat …
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