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{{Short description|The number of partitions of an integer}}
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[[File:Ferrer partitioning diagrams.svg|thumb|The values <math>p(1), \dots, p(8)</math> of the partition function (1, 2, 3, 5, 7, 11, 15, and 22) can be determined by counting the [[Young diagram]]s for the partitions of the numbers from 1 to 8.]]
In [[number theory]], the '''partition function''' {{math|''p''(''n'')}} represents the [[number]] of possible [[Integer partition|partitions]] of a non-negative integer {{mvar|n}}. For instance, {{math|1=''p''(4) = 5}} because the integer 4 has the five partitions {{math|1 + 1 + 1 + 1}}, {{math|1 + 1 + 2}}, {{math|1 + 3}}, {{math|2 + 2}}, and {{math|4}}.
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