Given a permutation p (of type permlist) of the integers 1 through n, for some n, the command nextperm returns the lexicographic successor of p.

If p is the lexicographically last permutation of degree n (that is, [n,n-1,...,2,1]), then the value FAIL is returned.

Given a permutation p (of type permlist) of the integers 1 through n, for some n, the command prevperm returns the lexicographic predecessor of p.

If p is the first permutation of degree n in lexicographic order (that is, [1,2,...,n-1,n]), then the value FAIL is returned.

The command firstperm returns the first permutation, in lexicographic order, of the permutations of the set {1,2,...,n} of integers from 1 to n. This is the permutation [ 1, 2, ..., n ].

The command lastperm returns the last permutation, in lexicographic order, of the permutations of the set {1,2,...,n} of integers from 1 to n. The lexicographically last permutation of {1,2,...,n} is [n, n-1, ..., 2, 1 ].

The combinat[nextperm], combinat[prevperm], combinat[firstperm] and combinat[lastperm] commands are thread-safe as of Maple 16.

For more information on thread safety, see index/threadsafe.

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

$\left[\mathrm{Chi}\,\mathrm{bell}\,\mathrm{binomial}\,\mathrm{cartprod}\,\mathrm{character}\,\mathrm{choose}\,\mathrm{composition}\,\mathrm{conjpart}\,\mathrm{decodepart}\,\mathrm{encodepart}\,\mathrm{eulerian1}\,\mathrm{eulerian2}\,\mathrm{fibonacci}\,\mathrm{firstcomb}\,\mathrm{firstpart}\,\mathrm{firstperm}\,\mathrm{graycode}\,\mathrm{inttovec}\,\mathrm{lastcomb}\,\mathrm{lastpart}\,\mathrm{lastperm}\,\mathrm{multinomial}\,\mathrm{nextcomb}\,\mathrm{nextpart}\,\mathrm{nextperm}\,\mathrm{numbcomb}\,\mathrm{numbcomp}\,\mathrm{numbpart}\,\mathrm{numbperm}\,\mathrm{partition}\,\mathrm{permute}\,\mathrm{powerset}\,\mathrm{prevcomb}\,\mathrm{prevpart}\,\mathrm{prevperm}\,\mathrm{randcomb}\,\mathrm{randpart}\,\mathrm{randperm}\,\mathrm{rankcomb}\,\mathrm{rankperm}\,\mathrm{setpartition}\,\mathrm{stirling1}\,\mathrm{stirling2}\,\mathrm{subsets}\,\mathrm{unrankcomb}\,\mathrm{unrankperm}\,\mathrm{vectoint}\right]$

$\mathrm{nextperm}\left(\left[1\,3\,2\right]\right)$

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

$\mathrm{nextperm}\left(\left[4\,3\,2\,1\right]\right)$

$\mathrm{FAIL}$

$\mathrm{prevperm}\left(\left[2\,1\,3\right]\right)$

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

$\mathrm{prevperm}\left(\left[1\,2\,3\,4\,5\right]\right)$

$\mathrm{FAIL}$

$\mathrm{firstperm}\left(4\right)$

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

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

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

The combinat[nextperm], combinat[prevperm], combinat[firstperm] and combinat[lastperm] commands were introduced in Maple 16.

For more information on Maple 16 changes, see Updates in Maple 16.