first partition in canonical partition sequence - Maple Help

Home : Support : Online Help : Mathematics : Discrete Mathematics : Combinatorics : combinat : combinat/firstpart

combinat[firstpart] - first partition in canonical partition sequence

combinat[nextpart] - next partition in canonical partition sequence

combinat[lastpart] - last partition in canonical partition sequence

combinat[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)