compile = truefalse

True means compile the iterator. The default is true.

rank = nonnegint

Specify the starting rank of the iterator. The default is one. Passing a value greater than one causes the iterator to skip the lower ranks; this can be useful when parallelizing iterators. 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.

If $n<t$, the iterator generates nothing.

If $n\&equals;t\&equals;0$, the iterator generates a single empty Array.

$\mathrm{with}\left(\mathrm{Iterator}\right)\&colon;$

$n,t≔5,3\&colon;$

$M≔\mathrm{Combination}\left(n\&comma;t\right)\&colon;$

$\mathrm{Print}\left(M\&comma;'\mathrm{showrank}'\right)\&colon;$

 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

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

$10$

$\mathrm{Unrank}\left(M\&comma;4\right)$

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

$N≔\mathrm{Object}\left(M\&comma;'\mathrm{rank}'=4\right)\&colon;$

$\mathrm{seq}\left(v\left[\right]\&comma;v=N\right)$

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

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.

The Iterator[Combination] command was updated in Maple 2022.

The n and t parameters were updated in Maple 2022.