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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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How to calculate an index into a binomial coefficient table from the underlying indexes
The following is a simple table that is bound by the binomial coefficient where N is 6 and K is 4. The total number of entries can be calculated as N! / ( K! (N - K)! ). So, 6! / (4! (6 - 4)!) = 15. …