Cycle (English)
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Definition (undergraduate level)
A permutation in which one subset of elements are moved cyclically and the remainder are not moved, such as
If γ is a cycle that permutes exactly l elements, then l is the length of the cycle, and γ has order l , that is γl=e where e is the identity permutation. Every permutation has a unique factorisation as a product of disjoint cycles.
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If γ is a cycle that permutes exactly l elements, then l is the length of the cycle, and γ has order l , that is γl=e where e is the identity permutation. Every permutation has a unique factorisation as a product of disjoint cycles.
Relations
- broader:
- (en) Physical thing
- narrower:
- (en) Canter
- references:
- (en) Circle
- referenced:
- (en) Circuit
- (en) Stirling numbers of the first kind
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