---
tag: PVSG53NFVQ
kind: concept
name: Cyclic order
aliases: [circular-order, circular-ordering, circularly-ordered-set, complete-cyclic-order, cyclic-ordering, cyclic-sequence, cyclically-ordered-set, l-cyclic-order, linear-cyclic-order, total-cyclic-order]
sources:
  - wikipedia: en:434673@r1374243991
    locator: Cyclic order
    note: adopted
    mention: wikipedia://en/434673
    sections: [Summary]
same_as:
  wikidata: Q5198223
  wikipedia: Cyclic order
inventory: [W32D4V6GJF]
---

## Summary

In mathematics, a **cyclic order** is a way to arrange a set of objects in a [[circle|060W5CBZP6]]. Unlike most structures in order theory, a cyclic order is not modeled as a [[binary relation|05AVARPXA2]], such as "$a < b$". One does not say that east is "more clockwise" than west. Instead, a cyclic order is defined as a ternary relation $[a, b, c]$, meaning "after $a$, one reaches $b$ before $c$". For example, \[June, October, February\], but not \[June, February, October\], cf. picture. A ternary relation is called a cyclic order if it is cyclic, asymmetric, transitive, and connected. Dropping the "connected" requirement results in a partial cyclic order.