---
tag: 5AGGEHCJ3Y
kind: concept
name: Solid partition
sources:
  - wikipedia: en:41305278@r1366593786
    locator: Solid partition
    note: adopted
    mention: wikipedia://en/41305278
    sections: [Summary]
same_as:
  wikidata: Q17149322
  wikipedia: Solid partition
inventory: [1JXXRY63HK]
---

## Summary

In mathematics, **solid partitions** are natural generalizations of [[integer partitions|0JV30XN73Z]] and plane partitions defined by Percy Alexander MacMahon. A solid partition of $n$ is a three-dimensional array of non-negative integers $n_{i,j,k}$ (with indices $i, j, k\geq 1$) such that