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Integer partitions

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Integer partitions

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04 Nov 2011 (Updated )

Finds all partitions of a set containing homogenous elements, also called integer partitions.

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Description

This is similar to submission "24185-partitions" in the exchange, but with the set containing identical elements. The partitioning is a also a way of writing the input n as a sum of positive integers.

An optional argument s can be supplied to output a subset of partitions with number of parts less than or equal to s.

The number of ways of partitioning is according to the sequence
http://oeis.org/A000041

Example 1: intpartition(4) gives {[1 1 1 1],[1 1 2],[1 3],[2 2],4}
Example 2: intpartition(10,2) gives {[3,7],[4,6],[5,5],10}

Required Products MATLAB
MATLAB release MATLAB 7.11 (R2010b)
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Updates
04 Nov 2011

corrected description

02 Dec 2013

--Added optional parameter s to specify maximum size of the partitions.
--Updated to more efficient code (~5x speed), as an unintended consequence, the ordering of partitions in the output cell is changed from the older version.

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