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.