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Calling Sequence
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PartitionPartCount(n, opts)
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Parameters
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n
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nonnegint; integer to partition
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opts
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(optional) equation(s) of the form option = value; specify options for the PartitionPartCount command
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Options
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True means compile the iterator. The default is true.
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Description
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The PartitionPartCount command returns an iterator that generates all partitions of the integer n in part-count form, in reverse lexicographic order.
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A partition of integer n in part-count form is a sequence of integers such that and for .
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The n parameter is the integer to partition.
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The output of the iterator is an array of fixed length n.
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Methods
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In addition to the common iterator methods, this iterator object has the following methods. The self parameter is the iterator object.
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Number(self): return the number of iterations required to step through the iterator, assuming it started at rank one.
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Examples
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Iterate through the partitions of 8.
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>
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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
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Compute the number of iterations.
Add the elements of each partition to verify they sum to n.
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| (2) |
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References
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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.
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Compatibility
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The Iterator[PartitionPartCount] command was introduced in Maple 2016.
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The Iterator[PartitionPartCount] command was updated in Maple 2022.
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The n parameter was updated in Maple 2022.
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