firstpart - Maple Help

combinat

 firstpart
 first partition in canonical partition sequence
 nextpart
 next partition in canonical partition sequence
 lastpart
 last partition in canonical partition sequence
 prevpart
 previous partition in canonical partition sequence

 Calling Sequence firstpart(n) nextpart(l) lastpart(n) prevpart(l)

Parameters

 l - partition; non-decreasing list of positive integers n - positive integer

Description

 • 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.

Examples

 > $\mathrm{with}\left(\mathrm{combinat}\right):$
 > $\mathrm{partition}\left(3\right)$
 $\left[\left[{1}{,}{1}{,}{1}\right]{,}\left[{1}{,}{2}\right]{,}\left[{3}\right]\right]$ (1)
 > $\mathrm{firstpart}\left(3\right)$
 $\left[{1}{,}{1}{,}{1}\right]$ (2)
 > $\mathrm{nextpart}\left(\right)$
 $\left[{1}{,}{2}\right]$ (3)
 > $\mathrm{nextpart}\left(\right)$
 $\left[{3}\right]$ (4)
 > $\mathrm{prevpart}\left(\right)$
 $\left[{1}{,}{2}\right]$ (5)
 > $\mathrm{lastpart}\left(3\right)$
 $\left[{3}\right]$ (6)