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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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binomial coefficients are integers because numerator and denominator form pairs?

I've heard of a claim that when calculating the binomial formula with integer input: $\mathrm{Bin}(n,k):=\prod^k_{i=1}\frac{n+1-i}{i}\in \mathbb{N}\ (\forall n,k\in\mathbb N)$ each denominator divides …
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