Crate stirling_numbers

Stirling numbers of the second kind and friends

For integers 0 ≤ k ≤ n, the Stirling number of the second kind S(n,k) is the number of k-element partitions of a set of size n. See wikipedia.

This crate consists of a few functions related to these Stirling numbers.

Functions

p_at_most_m_distinct_in_sample_of_x_from_n

Compute the probability of selecting at most m distinct elements in x random draws with replacement from a set of size n.
 

stirling2_ratio_table

Compute a table of “Stirling ratios”, Stirling numbers divided by the asympotic approximation k^n / k!, which is useful because the ratios are numerically better behaved than the Stirling numbers themselves.
 

stirling2_table

Build a table of Stirling numbers of the second kind S(n,k), for n ≤ n_max.