Definition:Cycle


 * Group Theory:
 * Cyclic Permutation: A permutation $\rho$ such that $\rho^k \left({i}\right) = i$ and $\rho$ fixes each $j$ not in $\left\{{i, \rho \left({i}\right), \ldots, \rho^{k-1} \left({i}\right)}\right\}$.
 * Also see Cycle notation.


 * Graph Theory:
 * Cycle: A circuit in which no vertex except the first appears more than once.


 * Abstract Algebra:
 * Cycle (Homology)


 * Topology:
 * Loop (Topology)


 * Differential Equations:
 * Cycle (Periodic Solution): A solution of a differential equation which is a periodic function.


 * Number Theory:
 * Cycle of a Periodic Continued Fraction.

Also see

 * Definition:Cyclic
 * Definition:Cocycle
 * Definition:Loop