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# IntegerPartitions

 IntegerPartitions[n]gives a list of all possible ways to partition the integer n into smaller integers. IntegerPartitionsgives partitions into at most k integers. IntegerPartitionsgives partitions into exactly k integers. IntegerPartitionsgives partitions into between and integers. IntegerPartitionsgives partitions involving only the . IntegerPartitionslimits the result to the first m partitions.
• n and the can be rational numbers, and can be negative.
• In the list of partitions, those involving earlier are given last.
All partitions of 5:
All partitions of 5:
 Out[1]=
 Scope   (3)
Partitions of 8 into at most 3 integers:
Partitions of 8 into exactly 3 integers:
Find all partitions of 8 that involve only 1, 2, and 5:
Find partitions of 6 of even length only:
Find ways to form 3 from combinations of rational numbers:
Find partitions involving negative numbers:
Find the first 10 partitions of 15:
Find the last 3 partitions of 15:
 Applications   (2)
Find the ways to make change for 156 cents with 10 or fewer standard coins:
Find "McNugget partitions" for 50:
Find the number of "McNugget partitions" for numbers up to 50:
Show integers that are not "McNuggetable":
The last case is exactly the corresponding Frobenius number:
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:
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:
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