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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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Show that this ratio of factorials is always an integer
show the formula always gives an integer
$$\frac{(2m)!(2n)!}{m!n!(m+n)!}$$
I don't remember where I read this problem, but it said this can be proved using a simple counting argument (like observing …