# Wolfram Language & System 10.4 (2016)|Legacy Documentation

This is documentation for an earlier version of the Wolfram Language.
BUILT-IN WOLFRAM LANGUAGE SYMBOL

# 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 and integers.

IntegerPartitions[n,kspec,{s1,s2,}]
gives partitions involving only the .

IntegerPartitions[n,kspec,sspec,m]
limits the result to the first m partitions.

## DetailsDetails

• Results from IntegerPartitions are normally given in reverse lexicographic order.
• Length[IntegerPartitions[n]] is PartitionsP[n].
• is equivalent to .
• IntegerPartitions[n,{kmin,kmax,dk}] gives partitions into , , integers.
• n and the can be rational numbers, and can be negative.
• In the list of partitions, those involving earlier are given last.
• IntegerPartitions[n,kspec,sspec,-m] limits the result to the last m partitions.
• In , a kspec of All corresponds to {0,Infinity}; an sspec of All corresponds to Range[n]; an m of All corresponds to Infinity.

## ExamplesExamplesopen allclose all

### Basic Examples  (1)Basic Examples  (1)

All partitions of 5:

 In[1]:=
 Out[1]=