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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 minimum set of combinations C(p,n) required to guarantee q<p matches with a targ...

You may find the following interesting. I think what you're asking for is the minimum cardinality of a code of length $p$ over the alphabet $Z_n$ (the integers mod $n$, assuming) the possible number …
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