compile = truefalse

True means compile the iterator. The default is true.

The MultiPartition command returns an iterator that generates all partitions of a multiset. A multiset is a generalization of a set; members are allowed to appear more than once.

The N parameter specifies the multiset to partition. It is a list of nonnegative integers, $\left[m_1\,\dots \,m_n\right]$, specifying the multiplicity of the distinct elements in the multiset.

The iterator returns an Array, $W$, with $W_{i,j}$ being the multiplicity of the i-th element in the j-th part of a partition. The number of nonzero columns, starting from the first, is given by the length method.

This iterator object has the common iterator methods.

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

$M≔\mathrm{MultiPartition}\left(\left[2\,3\right]\right)\:$

$\mathrm{Print}\left(M\,5\,'\mathrm{showrank}'\right)\:$

1: 2
   3

2: 2 0
   2 1

3: 2 0
   1 2

4: 2 0 0
   1 1 1

5: 2 0
   0 3

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, algorithm M, multipartitions in decreasing lexicographic order, pp. 75-76.  The algorithm was corrected; Knuth_errata, p. 75.

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

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

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

The N parameter was updated in Maple 2022.