Unlike most structures in order theory, a cyclic order is not modeled as a binary relation, such as " ".
22.
A cyclic order on is the same as a permutation that makes all of into a single action by a finite cyclic group.
23.
A ternary relation that satisfies the first three axioms, but not necessarily the axiom of totality, is a partial cyclic order.
24.
A token ring network can be modeled as a polling system where a single server provides service to queues in a cyclic order.
25.
In mathematics, a "'cyclic order "'is a way to arrange a set of objects in a circle.
26.
Choosing a linear order is equivalent to choosing a first element, so there are exactly linear orders that induce a given cyclic order.
27.
Any linear order can be bent into a circle, and any cyclic order can be cut at a point, resulting in a line.
28.
Two hyperbolic n-gons having the same angles in the same cyclic order may have different edge lengths and are not in general congruent.
29.
The real projective line has a cyclic order which is an important mathematical structure in showing that the real line is totally ordered and complete.
30.
One can also construct partial cyclic orders with higher-order obstructions such that, for example, any 15 triples can be added but the 16th cannot.
