Stirling2

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.

partitions

A set of tools to permute multisets without loops or hash tables and to generate integer partitions. The permutation functions are based on C code from Aaron Williams. Cool-lex order is similar to colexicographical order. The algorithm is described in Williams, A. Loopless Generation of Multiset Permutations by Prefix Shifts. SODA 2009, Symposium on Discrete Algorithms, New York, United States. The permutation code is distributed without restrictions. The code for stable and efficient computation of multinomial coefficients comes from Dave Barber. The code can be download from <http://tamivox.org/dave/multinomial/index.html> and is distributed without conditions. The package also generates the integer partitions of a positive, non-zero integer n. The C++ code for this is based on Python code from Jerome Kelleher which can be found here <https://jeromekelleher.net/category/combinatorics.html>. The C++ code and Python code are distributed without conditions.

James Curran

multicool

Permutations of Multisets in Cool-Lex Order

Stirling2 function

<dl><dt>n</dt>
<dd>A vector of one or more positive integers</dd>
<dt>k</dt>
<dd>A vector of one or more positive integers</dd></dl>

Arguments

<ul>
<li><code>S2()</code>: Compute Stirling numbers of the second kind</li>
</ul>

Functions

Author

Compute Stirling numbers of the second kind — Stirling2

<dl>

<dt>n</dt>
<dd>A vector of one or more positive integers</dd>


<dt>k</dt>
<dd>A vector of one or more positive integers</dd>

</dl>

Stirling2: Compute Stirling numbers of the second kind

Description

Usage

Value

Arguments

Functions

Author

Details

References

Examples