compile = truefalse

True means compile the iterator. The default is true.

rank = nonnegint

Specify the starting rank of the iterator. The default is one. The starting rank reverts to one when the iterator is reset, reused, or copied.

The Combination command returns an iterator that generates all t-combinations of the integers $0..n-1$.

The combinations, when read from right to left, appear in lexicographic order.

The n parameter is the size of the set.

The t parameter is the number of elements in each combination; it must be less than or equal to n.

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

$n,t≔5,3\:$

$M≔\mathrm{Combination}\left(n\,t\right)\:$

$\mathrm{Print}\left(M\,'\mathrm{showrank}'\right)\:$

 1: 0 1 2
 2: 0 1 3
 3: 0 2 3
 4: 1 2 3
 5: 0 1 4
 6: 0 2 4
 7: 1 2 4
 8: 0 3 4
 9: 1 3 4
10: 2 3 4

$\mathrm{Number}\left(M\right)$

$10$

$\mathrm{Unrank}\left(M\,4\right)$

$\left[\begin{array}{ccc}1& 2& 3\end{array}\right]$

$N≔\mathrm{Object}\left(M\,\mathrm{rank}=4\right)\:$

$\mathrm{seq}\left(v\left[\right]\,v=N\right)$

$\left[\begin{array}{ccc}1& 2& 3\end{array}\right],\left[\begin{array}{ccc}0& 1& 4\end{array}\right],\left[\begin{array}{ccc}0& 2& 4\end{array}\right],\left[\begin{array}{ccc}1& 2& 4\end{array}\right],\left[\begin{array}{ccc}0& 3& 4\end{array}\right],\left[\begin{array}{ccc}1& 3& 4\end{array}\right],\left[\begin{array}{ccc}2& 3& 4\end{array}\right]$

Knuth, Donald Ervin. The Art of Computer Programming, volume 4, fascicle 3; generating all combinations and partitions, sec. 7.2.1.3, algorithm T (Lexicographic combinations), p. 5.

The Iterator[Combination] command was introduced in Maple 2016.

For more information on Maple 2016 changes, see Updates in Maple 2016.