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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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Im looking for an algorithm that can solve or approximate the solution to a problem

Let me first explain the problem using an analogy. Let's say you have $N$ doors and $M$ keys. Each door can be opened with a combination of keys, each combination is also unique (i.e. there aren't be …
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