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Cyclic order

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 , meaning "after a, one reaches b before c". For…

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Overview

Finite cycles

Definitions

Monotone functions

Further constructions

Topology

Related structures

Symmetries and model theory

Cognition

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Map overview Semantic statistics

Cyclic order

Nodes133
Edges132
Triples85
Avg. degree1.99
Density0.015038
Components1

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Cyclic order

Top relations

related to Notes on usage · 13
Cyclic order → All, Bowditch, Cohn, Finally, Giraudet, Holland, Huntington, Isli, Kok, Mosher, Novák, Some, The
related to Definitions · 10
Cyclic order → An, By, For, However, Important, Instead, Nor, S1, The, Traveling
related to Groups · 9
Cyclic order → Archimedean, Cyclically, Every, If, Ladislav Rieger, Since, Some, They, Z/n
related to Functions on finite sets · 7
Cyclic order → Alain Connes, Cyclohedra, Examining, In, S1, The, There
related to Modified axioms · 7
Cyclic order → An, Appropriately, CC, Instead, It, One, Replacing
related to The ternary relation · 7
Cyclic order → Asymmetry, Connectedness, Cyclicity, If, The, Transitivity, X3
related to Automorphisms · 5
Cyclic order → As, C2, Coxeter, If, The
related to Finite cycles · 5
Cyclic order → Alternatively, Another, Each, There, Zn-torsor
related to Intervals · 5
Cyclic order → An, As, Given, One, The
related to Topology · 5
Cyclic order → Discrete, Interesting, Lorentz, The, To

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Important terminology

cyclic order set ordered relation cyclically linear one called circle cycle orders example also groups ternary cycles elements finite may

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Cyclic orderis away to arrange a set of objects in a circle0.90text
Cyclic orderis aternary relation that generalizes a0.90text
Cyclic orderrelated to AutomorphismsAs0.60section
Cyclic orderrelated to AutomorphismsIf0.60section
Cyclic orderrelated to AutomorphismsCoxeter0.60section
Cyclic orderrelated to AutomorphismsThe0.60section
Cyclic orderrelated to AutomorphismsC20.60section
Cyclic orderrelated to CognitionHans Freudenthal0.60section
Cyclic orderrelated to CognitionJean Piaget0.60section
Cyclic orderrelated to CognitionSome0.60section
Cyclic orderrelated to DefinitionsAn0.60section
Cyclic orderrelated to DefinitionsImportant0.60section

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