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The procedure partition partitions an integer n into all possible sums without regard to order. The output is a list of lists of integers where the sum of the elements in each list is n.

See the function numbpart , which computes the number of partitions.

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

$\mathrm{with}\left(\mathrm{combinat}\,\mathrm{partition}\right)$

$\left[\mathrm{partition}\right]$

$\mathrm{partition}\left(0\right)$

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

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

$\mathrm{partition}\left(6\,3\right)$

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