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In [[number theory]], the '''partition function''' p(''n'') represents the [[number]] of possible [[integer partition|partitions]] of a [[natural number]] ''n'', which is to say the number of distinct (and order independent) ways of representing ''n'' as a [[sum]] of natural numbers. For example, 4 can be partitioned in 5 distinct ways
:4, 3+1, 2+2, 2+1+1, 1+1+1+1
So p(4) = 5. By convention p(0) = 1, p(''n'') = 0 for ''n'' negative. Partitions can be graphically visualized with [[Young diagram]]s. They occur in a number of branches of [[mathematics]] and [[physics]], including the study of [[symmetric polynomial]]s and in [[group representation|group representation theory]].
==Intermediate function==
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