The number of partitions of an integer - Maple Help

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combinat[numbpart] - The number of partitions of an integer

Calling Sequence

numbpart(n, m)

Parameters

n

-

non-negative integer; integer to partition

m

-

(optional) non-negative integer; maximum integer in partitions

Description

• 

This procedure counts the number of partitions of an integer n, that is, the number of ways n can be split into sums without regard to order.

• 

See the partition function that constructs the partitions. Note that numbpart(n) = nops(partition(n)) for 0n.

• 

The command with(combinat,numbpart) allows the use of the abbreviated form of this command.

Examples

withcombinat:

numbpart5

7

(1)

partition5

1,1,1,1,1,1,1,1,2,1,2,2,1,1,3,2,3,1,4,5

(2)

numbpart6,3

7

(3)

partition6,3

1,1,1,1,1,1,1,1,1,1,2,1,1,2,2,2,2,2,1,1,1,3,1,2,3,3,3

(4)

See Also

combinat[partition]


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