Given a combination (subset) s of the integers from 1 to n, for some positive integer n, the command rankcomb( 's', 'n' ) computes the lexicographic rank of s.  That is, if s has k members, and if the k-subsets of {1,2,...,n} are listed lexicographically, then the position of the given subset in this ordered list is returned.

Given a rank r (where r is at most binomial(n,k)), the command unrankcomb( 'r', 'n', 'k' ) computes the k-subset of {1,2,...,n} which occurs in the r-th place in a lexicographically ordered list of the k-subsets of {1,2,...,n}.

The commands rankcomb and unrankcomb are inverse to one another in the sense that they satisfy rankcomb( unrankcomb( r, k, n ), n ) = r and unrankcomb( rankcomb( s, n ), nops( s ), n ) = s.

The combinat[rankcomb] and combinat[unrankcomb] commands are thread-safe as of Maple 16.

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

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

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

$7$

$\mathrm{rankcomb}\left(\left\{2\,3\,4\right\}\,9\right)$

$29$

$\mathrm{unrankcomb}\left(29\,9\,3\right)$

$\left\{2\,3\,4\right\}$

The combinat[rankcomb] and combinat[unrankcomb] commands were introduced in Maple 16.

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