compile = truefalse

True means compile the iterator. The default is true.

The SetPartitionFixedSize command returns an iterator that generates fixed-size partitions of the set of integers starting at one. A partition of a set is a division of the set into disjoint subsets whose union is the set. A fixed-size partition fixes the sizes and number of the partitions.

The s parameter is a list of nonnegative integers that specify the size of each subset of a partition. Any zeros in s have no effect on the output.

The iterator output is a permutation of the integers from one to n, where n is the sum of the sizes of the subsets. Let $S_k=1+\left(\sum _{j=1}^{k-1}{s}_j\right)$, then the k-th subset corresponds to the indices $S_k..S_{k+1}-1$.

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

$F≔\mathrm{SetPartitionFixedSize}\left(\left[2\,1\,2\right]\right)\:$

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

 1: 1 2 3 4 5
 2: 1 2 4 3 5
 3: 1 2 5 3 4
 4: 1 3 4 2 5
 5: 1 3 5 2 4
 6: 1 4 5 2 3
 7: 1 3 2 4 5
 8: 1 4 2 3 5
 9: 1 5 2 3 4
10: 1 4 3 2 5
11: 1 5 3 2 4
12: 1 5 4 2 3
13: 2 3 1 4 5
14: 2 4 1 3 5
15: 2 5 1 3 4

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

$15$

Knuth, Donald Ervin. The Art of Computer Programming, volume 4, fascicle 3; generating all combinations and partitions, sec. 7.2.1.5, generating all set partitions, fixed sizes, exercise 6, pp. 78 and 125.

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

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

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

The s parameter was updated in Maple 2022.