IntegerPartitions

IntegerPartitions[n]
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, {k_min, k_max}]
gives partitions into between k_min and k_max integers.

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

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

Results from IntegerPartitions are normally given in reverse lexicographic order.

IntegerPartitions[n, {k_min, k_max, dk}] gives partitions into k_min, k_min+dk, ... integers.

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.

All partitions of 5: