## PARTITIONS

version 1.1.0.0 (3.79 KB) by
Finds all partitions of a set, or only those partitions of a specified length. Includes a viewer.

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Updated 21 May 2009

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C = PARTITIONS(N), for scalar N, returns all possible partitions of the set given by {1,2,3,...N}.
C = PARTITIONS(N), for vector N, returns the partitions of the vector elements, treated as members of a set.
C = PARTITIONS(N), for cell N, returns the partitions of the cell
elements treated as members of a set.

PARTITIONS(N,K) returns only the partitions of length K.
The results are stored in a cell array. For example:

The 15 partitions set {1 2 3 4}:
{1 2 3 4}
{1 2 3} {4}
{1 2 4} {3}
{1 2} {3 4}
{1 2} {3} {4}
{1 3 4} {2}
{1 3} {2 4}
{1 3} {2} {4}
{1 4} {2 3}
{1} {2 3 4}
{1} {2 3} {4}
{1 4} {2} {3}
{1} {2 4} {3}
{1} {2} {3 4}
{1} {2} {3} {4}

Also included is a viewer function, PARTDISP, which allows for easy viewing of the partitions. The output is a string to the command window.

C = partitions({'peanut','butter','yummy'});
partdisp(C)

The 5 partitions of set {peanut butter yummy}:
{peanut butter yummy}
{peanut butter} {yummy}
{peanut yummy} {butter}
{peanut} {butter yummy}
{peanut} {butter} {yummy}

Please: READ THE HELP BEFORE USING.
Please email me if bugs are found in the code.
Thanks.

### Cite As

Matt Fig (2022). PARTITIONS (https://www.mathworks.com/matlabcentral/fileexchange/24185-partitions), MATLAB Central File Exchange. Retrieved .

##### MATLAB Release Compatibility
Created with R2007a
Compatible with any release
##### Platform Compatibility
Windows macOS Linux
##### Acknowledgements

Inspired by: Set partition

Inspired: Set partition

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