All four of the functions use the canonical partition sequence defined by combinat[encodepart].

Given a positive integer n, firstpart(n) computes and returns the first partition of n in the canonical partition sequence.

Given a partition l of n, nextpart(l) computes and returns the next partition of n in the canonical partition sequence.

Given a positive integer n, lastpart(n) computes and returns the last partition of n in the canonical partition sequence.

Given a partition l of n, prevpart(l) computes and returns the previous partition of n in the canonical partition sequence.

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

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

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

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

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

$\mathrm{nextpart}\left(\right)$

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

$\mathrm{nextpart}\left(\right)$

$\left[3\right]$

$\mathrm{prevpart}\left(\right)$

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

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

$\left[3\right]$