Given a combination p (of type set(posint)) of k integers chosen from {1,2, ..., n }, for some n, the command nextcomb returns the lexicographic successor of s.

If s is the lexicographically last combination (that is, { n - k + 1, n - k + 2, ..., n}), then the value FAIL is returned.

Given a combination s (of type set(posint)) of k  integers chosen from {1,2, ..., n }, for some n, the command prevcomb returns the lexicographic predecessor of s.

If s is the lexicographically first combination (that is, {1,2, ..., k}), then the value FAIL is returned.

The firstcomb command returns the lexicographically first combination of k elements chosen from {1, 2, ..., n }. This is the subset {1,2, ..., k}.

The lastcomb command returns the lexicographically last combination of k elements chosen from {1,2, ..., n }, which is { n - k + 1, n - k + 2, ..., n }.

The combinat[nextcomb], combinat[prevcomb], combinat[firstcomb] and combinat[lastcomb] commands are thread-safe as of Maple 16.

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

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

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

$\mathrm{nextcomb}\left(\left\{1\,2\,3\right\}\,5\right)$

$\left\{1\,2\,4\right\}$

$\mathrm{nextcomb}\left(\left\{1\,2\,3\,4\right\}\,4\right)$

$\mathrm{FAIL}$

$\mathrm{prevcomb}\left(\left\{2\,3\,4\right\}\,5\right)$

$\left\{1\,4\,5\right\}$

$\mathrm{prevcomb}\left(\left\{1\,2\,3\,4\,5\right\}\,5\right)$

$\mathrm{FAIL}$

$\mathrm{firstcomb}\left(5\,3\right)$

$\left\{1\,2\,3\right\}$

$\mathrm{lastcomb}\left(5\,3\right)$

$\left\{3\,4\,5\right\}$

The combinat[nextcomb], combinat[prevcomb], combinat[firstcomb] and combinat[lastcomb] commands were introduced in Maple 16.

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