This function calculates the number of permutations of a multiset, this being the multinomial coefficient. If a set X contains k unique elements x_1, x_2, …, x_k with associate counts (or multiplicities) of n_1, n_2, …, n_k, then this function returns

This function computes Stirling numbers of the second kind, S(n, k), which count the number of ways of partitioning n distinct objects in to k non-empty sets.

This function will return either all, or a length restricted subset of the integer partitions of an integer n. The method works by considering compositions rather than partions, hence the name.