Cyclic order

Summary

In mathematics, a cyclic order is a way to arrange a set of objects in a circle. Unlike most structures in order theory, a cyclic order is not modeled as a binary relation, 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.