The procedure composition computes and returns a list containing all distinct ordered k-tuples of positive integers whose elements sum to n.  These are known as the compositions of n.

In the list of k-tuples returned, each k-tuple is a list representing a particular composition of n.

See also the function numbcomp, which computes the number of different compositions of an integer.

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

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

$\mathrm{composition}\left(5\,2\right)$

$\left\{\left[1\,4\right]\,\left[2\,3\right]\,\left[3\,2\right]\,\left[4\,1\right]\right\}$

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

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

$\mathrm{composition}\left(4\,3\right)$

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