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Set partition

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Set partition

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16 May 2009 (Updated )

List all partitions a set n elements

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Description

A set of of n elements can be partitioned in non empty subsets.

This package provide function to list all possible partitions. The number of partition is Bell's number.

The number of subsets that composed the partitions can be optionally specified. The number of partition is Stirling's number of the second kind.

Acknowledgements

This file inspired Partitions.

MATLAB release MATLAB 7.8 (R2009a)
Other requirements Should work on most recent MATLAB releases
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Comments and Ratings (4)
20 Apr 2012 Alessandro

Is there an easy way to generate the partitions incrementally? I mean I'd like to use it for big N so it would be great if there was a way to generate a different partition a time, because of space limits.

Thanks!

18 May 2009 Matt Fig

Very nice: smartly coded, fast, well implemented.

18 May 2009 Bruno Luong

Darren, thank you for the suggestion. I'll add an example of usage. Functions with more efficient engine will be soon upgraded.

17 May 2009 Darren Rowland

At last someone has implemented this functionality. Excellent!
I would only suggest that an example of usage and output could be helpful in the SetPartition file and that the first few lines of Bell and Stirling2nd could be rearranged to give meaningful H1 lines.

Updates
17 May 2009

Improve engine and example usage in the help as suggested Darren Rowland

19 May 2009

Correct a BUG for N=0. Minor speed improvement.

23 May 2009

Possibility to partition generic set elements (following Matt Fig's idea). New function to replace elements of a standard set partitioning list

02 Jun 2009

Partitions display function

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