In mathematics, and in particular in group theory, a cycle is a permutation of the elements of some set X which maps the elements of some subset S to each other in a cyclic fashion, while fixing (i.e. , mapping to themselves) all other elements. The set S is called the orbit of the cycle.

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  • In mathematics, and in particular in group theory, a cycle is a permutation of the elements of some set X which maps the elements of some subset S to each other in a cyclic fashion, while fixing (i.e. , mapping to themselves) all other elements. The set S is called the orbit of the cycle.
  • Nechť <math>\{r_1, r_2, ... , r_k\}</math> je podmnožina množiny <math>M = \{ 1, 2, ... , n\}</math>, kde <math>k > 1</math>. Pak takovou permutaci <math>\pi</math>, pro niž platí <math>\pi(r_1)=r_2, \pi(r_2)=r_3, ... , \pi(r_k - 1)=r_k, \pi(r_k)=r_1</math> a <math>\pi(s)=s</math> pro <math>s \in M - \{r_1,r_2,... ,r_k\}</math>, nazýváme cyklem délky <math>k</math> a označujeme <math>(r_1, r_2, ... , r_k)</math>. Cyklus délky 2 se nazývá transpozicí.
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  • 2262 (xsd:integer)
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  • Chain complex Fundamental terminology
  • Cycle (graph theory)
  • cycles in graph theory
  • cycles in homological algebra
  • group theory
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  • cycle
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  • In mathematics, and in particular in group theory, a cycle is a permutation of the elements of some set X which maps the elements of some subset S to each other in a cyclic fashion, while fixing (i.e. , mapping to themselves) all other elements. The set S is called the orbit of the cycle.
  • Nechť <math>\{r_1, r_2, ... , r_k\}</math> je podmnožina množiny <math>M = \{ 1, 2, ... , n\}</math>, kde <math>k > 1</math>. Pak takovou permutaci <math>\pi</math>, pro niž platí <math>\pi(r_1)=r_2, \pi(r_2)=r_3, ... , \pi(r_k - 1)=r_k, \pi(r_k)=r_1</math> a <math>\pi(s)=s</math> pro <math>s \in M - \{r_1,r_2,...
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  • Cycle (mathematics)
  • Cyklus (algebra)
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