Bell

This function computes the Bell numbers, which is the summ of Stirling
numbers of the second kind, $S(n, k)$, over $k = 1,\ldots,
n$, i.e. $$B_n = \sum_{k=1}^{n}S(n, k),n \ge 1$$

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

Bell function

<dl><dt>n</dt>
<dd>A vector of one or more non-zero positive integers</dd></dl>

Arguments

<ul>
<li><code>B()</code>: Compute the Bell numbers</li>
</ul>

Functions

Author

Compute the Bell numbers — Bell

<dl>

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

</dl>

Bell: Compute the Bell numbers

Description

Usage

Value

Arguments

Functions

Author

References

See Also

Examples