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The functions encodepart and decodepart provide a canonical labeling of all the partitions of n.

Given a partition l of n, encodepart(l) computes and returns the integer m between $1$ and numbpart(n) uniquely representing this partition.

Given a positive integer n and a positive integer m between $1$ and numbpart(n) the function decodepart(m, n) computes and returns the unique partition l represented by this positive integer.

The command with(combinat,encodepart) allows the use of the abbreviated form of this command.

$\mathrm{with}\left(\mathrm{combinat}\right)\:$

$\mathrm{partition}\left(3\right)$

$\left[\left[1\,1\,1\right]\,\left[1\,2\right]\,\left[3\right]\right]$

$\mathrm{decodepart}\left(3\,1\right)$

$\left[1\,1\,1\right]$

$\mathrm{decodepart}\left(3\,2\right)$

$\left[1\,2\right]$

$\mathrm{decodepart}\left(3\,3\right)$

$\left[3\right]$

$\mathrm{encodepart}\left(\left[1\,2\right]\right)$

$2$