---
tag: 1Y8SFRWEKK
kind: concept
name: Ordered Bell number
aliases: [fubini-number, fubini-numbers, horse-numbers]
sources:
  - wikipedia: en:6992164@r1347722029
    locator: Ordered Bell number
    note: adopted
    mention: wikipedia://en/6992164
    sections: [Summary]
same_as:
  wikidata: Q7100706
  wikipedia: Ordered Bell number
inventory: [GG4J5EMN9D]
---

## Summary

In number theory and enumerative combinatorics, the **ordered Bell numbers** or **Fubini numbers** count the weak orderings on a [[set|0BSJ7RQ9BW]] of $n$ elements. Weak orderings arrange their elements into a sequence allowing ties, such as might arise as the outcome of a horse race.