# 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].
• is equivalent to .
• 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 , 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 all

## Basic Examples(1)

All partitions of 5:

 In[1]:=
 Out[1]=