Partition function (number theory)

From Citizendium
Revision as of 16:32, 13 December 2008 by imported>Richard Pinch (moving References to Bibliography)
Jump to navigation Jump to search
This article is a stub and thus not approved.
Main Article
Discussion
Related Articles  [?]
Bibliography  [?]
External Links  [?]
Citable Version  [?]
 
This editable Main Article is under development and subject to a disclaimer.

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