Cycle (mathematics)
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High Quality Content by WIKIPEDIA articles! 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.One of the basic results on symmetric groups says that any permutation can be expressed as product of disjoint cycles (more precisely: cycles with disjoint orbits); such cycles commute with each other, and the expression of the permutation is unique up to the order of...
High Quality Content by WIKIPEDIA articles! 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.One of the basic results on symmetric groups says that any permutation can be expressed as product of disjoint cycles (more precisely: cycles with disjoint orbits); such cycles commute with each other, and the expression of the permutation is unique up to the order of the cycles (but note that the cycle notation is not unique: each k-cycle can itself be written in k different ways, depending on the choice of s0 in its orbit).
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