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Cyclic order — Wikipedia (en)

Source: Wikipedia (en)
Original: https://en.wikipedia.org/wiki/Cyclic_order
License (as archived): CC-BY-SA-4.0
Archived: 2026-10-06T16:44:25.818Z
SHA-256 of the archived text: 61a75d07e81f7d08d2e58a14cbc2a9e1bb3d54083ec87548e62ed9e1a0265b48
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Cyclic order — Wikipedia (en) — Wikipedia (en), https://en.wikipedia.org/wiki/Cyclic_order (CC-BY-SA-4.0); archived copy: https://metraipolis.com/documento/dc_aeda76e63dbf (Metraipolis archive dc_aeda76e63dbf, sha256 61a75d07e81f7d08d2e58a14cbc2a9e1bb3d54083ec87548e62ed9e1a0265b48)

BibTeX

@misc{dcaeda76e63dbf,
  title = {Cyclic order — Wikipedia (en)},
  howpublished = {Wikipedia (en)},
  url = {https://en.wikipedia.org/wiki/Cyclic_order},
  note = {License CC-BY-SA-4.0; archived copy https://metraipolis.com/documento/dc_aeda76e63dbf; sha256 61a75d07e81f7d08d2e58a14cbc2a9e1bb3d54083ec87548e62ed9e1a0265b48},
  year = {2026}
}

Archived text

Reproduced under CC-BY-SA-4.0. Attribution: Wikipedia (en), https://en.wikipedia.org/wiki/Cyclic_order. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

In mathematics, a cyclic order is a way to arrange a set of objects in a circle.[nb] 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. A set with a cyclic order is called a cyclically ordered set or simply a cycle.[nb] Some familiar cycles are discrete, having only a finite number of elements: there are seven days of the week, four cardinal directions, twelve notes in the chromatic scale, and three plays in rock-paper-scissors. In a finite cycle, each element has a "next element" and a "previous element". There are also cyclic orders with infinitely many elements, such as the oriented unit circle in the plane. Cyclic orders are closely related to the more familiar linear orders, which arrange objects in a line. Any linear order can be bent into a circle, and any cyclic order can be cut at a point, resulting in a line. These operations, along with the related constructions of intervals and covering maps, mean that questions about cyclic orders can often be transformed into questions about linear orders. Cycles have more symmetries than linear orders, and they often naturally occur as residues of linear structures, as in the finite cyclic groups or the real projective line.

Tema degli esploratori: matematica e informatica teorica (deposito sistematico; categoria «Combinatorics»).
Fonte: Wikipedia in inglese, voce «Cyclic order» — https://en.wikipedia.org/wiki/Cyclic_order
Wikidata Q5198223 (dati Wikidata in CC0 1.0) — https://www.wikidata.org/wiki/Q5198223
Autori: i contributori di Wikipedia (cronologia: https://en.wikipedia.org/wiki/Cyclic_order?action=history).
Licenza: Creative Commons Attribuzione-Condividi allo stesso modo 4.0 (CC BY-SA 4.0) — https://creativecommons.org/licenses/by-sa/4.0/. Il riuso richiede attribuzione e stessa licenza.
Estratto dell'introduzione non modificato nel contenuto; revisione 1374243991, consultata il 2026-10-06T15:18:47.042Z tramite l'API ufficiale di Wikipedia. Impronta SHA-256 dell'estratto: 7ea220e7acfc260011c7b42d329bad4083caed62bc66abe675fd950ff4cad0c6