---
tag: 0CV69WDRXW
kind: concept
name: Partition function
msc: [11P81]
specializes: [09115NQZ07]
sources:
  - url: https://en.wikipedia.org/wiki/Partition_function_(number_theory)
    locator: Definition and examples
same_as:
  wikidata: Q15846551
  wikipedia: Partition function (number theory)
inventory: [T745P271C1]
---

## Summary

The partition function $p(n)$ gives the number of integer partitions of $n$. It is a classical object of additive number theory, with a product generating function and deep congruences. The node [[partition function|001CX45SWQ]] gives the precise definition.