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Partition function (number theory)

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In number theory the partition function p(n) counts the number of partitions of a positive integer n, that is, the number of ways of expressing n as a sum of positive integers (where order is not significant).

Thus p(3) = 3, since the number 3 has 3 partitions:

  • 3
  • 2+1
  • 1+1+1

Properties

The partition function satisfies an asymptotic relation