compile = truefalse

True means compile the iterator. The default is true.

The PartitionPartCount command returns an iterator that generates all partitions of the integer n in part-count form, in reverse lexicographic order.

A partition of integer n in part-count form is a sequence of integers $\left(c_1\,\dots \,c_n\right)$ such that $n\=\sum _{k\=1}^{n}k{c}_k$ and $0\le c_k\le n$ for $k\in \left\{1\,\dots \,n\right\}$.

The n parameter is the integer to partition.

The output of the iterator is an array of fixed length n.

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

$n≔8\:$

$P≔\mathrm{PartitionPartCount}\left(n\right)\:$

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

 1: 8 0 0 0 0 0 0 0
 2: 6 1 0 0 0 0 0 0
 3: 4 2 0 0 0 0 0 0
 4: 2 3 0 0 0 0 0 0
 5: 0 4 0 0 0 0 0 0
 6: 5 0 1 0 0 0 0 0
 7: 3 1 1 0 0 0 0 0
 8: 1 2 1 0 0 0 0 0
 9: 2 0 2 0 0 0 0 0
10: 0 1 2 0 0 0 0 0
11: 4 0 0 1 0 0 0 0
12: 2 1 0 1 0 0 0 0
13: 0 2 0 1 0 0 0 0
14: 1 0 1 1 0 0 0 0
15: 0 0 0 2 0 0 0 0
16: 3 0 0 0 1 0 0 0
17: 1 1 0 0 1 0 0 0
18: 0 0 1 0 1 0 0 0
19: 2 0 0 0 0 1 0 0
20: 0 1 0 0 0 1 0 0
21: 1 0 0 0 0 0 1 0
22: 0 0 0 0 0 0 0 1

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

$22$

$\mathrm{seq}\left(\mathrm{add}\left(kp\left[k\right]\,k=1..n\right)\,p=P\right)$

$8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8$

Knuth, Donald Ervin. The Art of Computer Programming, volume 4, fascicle 3; generating all combinations and partitions, sec. 7.2.1.4, generating all partitions, algorithm C, p. 110, ex. 5.

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

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

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

The n parameter was updated in Maple 2022.