---
tag: 7EQJMZTAFY
kind: concept
name: Triangle of partition numbers
sources:
  - wikipedia: en:70784332@r1270071975
    locator: Triangle of partition numbers
    note: adopted
    mention: wikipedia://en/70784332
    sections: [Summary]
same_as:
  wikidata: Q112160911
  wikipedia: Triangle of partition numbers
inventory: [28EV2YFEVR]
---

## Summary

In the number theory of [[integer partitions|0JV30XN73Z]], the numbers $p_k(n)$ denote both the number of partitions of $n$ into exactly $k$ parts (that is, sums of $k$ positive integers that add to $n$), and the number of partitions of $n$ into parts of maximum size exactly $k$. These two types of partition are in [[bijection|0GG9TVW90M]] with each other, by a diagonal reflection of their Young diagrams. Their numbers can be arranged into a triangle, the **triangle of partition numbers**, in which the $n$th row gives the partition numbers $p_1(n), p_2(n), \dots, p_n(n)$: