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.

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

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

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

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

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

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

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