IntegerPartitions
gives a list of all possible ways to partition the integer n into smaller integers.
IntegerPartitions[n,k]
gives partitions into at most k integers.
IntegerPartitions[n,{k}]
gives partitions into exactly k integers.
IntegerPartitions[n,{kmin,kmax}]
gives partitions into between kmin and kmax integers.
IntegerPartitions[n,kspec,{s1,s2,…}]
gives partitions involving only the si.
IntegerPartitions[n,kspec,sspec,m]
limits the result to the first m partitions.
Details
- Results from IntegerPartitions are normally given in reverse lexicographic order.
- Length[IntegerPartitions[n]] is PartitionsP[n].
- IntegerPartitions[n] is equivalent to IntegerPartitions[n,All].
- IntegerPartitions[n,{kmin,kmax,dk}] gives partitions into kmin, kmin+dk, … integers.
- n and the si can be rational numbers, and can be negative.
- In the list of partitions, those involving earlier si are given last.
- IntegerPartitions[n,kspec,sspec,-m] limits the result to the last m partitions.
- In IntegerPartitions[n,kspec,sspec,m], a kspec of All corresponds to {0,Infinity}; an sspec of All corresponds to Range[n]; an m of All corresponds to Infinity.
Examples
open allclose allScope (3)
Generalizations & Extensions (4)
Applications (2)
Properties & Relations (4)
Each sublist adds up to the original number:
The length of IntegerPartitions[n] is PartitionsP[n]:
IntegerPartitions gives results in reverse lexicographic order, not Sort order:
For integers below 10, generate IntegerPartitions order by converting to strings:
FrobeniusSolve gives coefficient lists for IntegerPartitions:
Possible Issues (3)
IntegerPartitions cannot give an infinite list of partitions:
There are no integer partitions of 1/2:
There are, however, partitions into rationals:
If all items requested by the fourth argument are not present, a warning message is issued:
To suppress the message, use Off:
Text
Wolfram Research (2007), IntegerPartitions, Wolfram Language function, https://reference.wolfram.com/language/ref/IntegerPartitions.html (updated 2008).
CMS
Wolfram Language. 2007. "IntegerPartitions." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2008. https://reference.wolfram.com/language/ref/IntegerPartitions.html.
APA
Wolfram Language. (2007). IntegerPartitions. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/IntegerPartitions.html