Category:Cyclic Permutations

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This category contains results about Cyclic Permutations.
Definitions specific to this category can be found in Definitions/Cyclic Permutations.

Let $S_n$ denote the symmetric group on $n$ letters.

Let $\rho \in S_n$ be a permutation on $S$.


Then $\rho$ is a cyclic permutation of length $k$ if and only if there exists $k \in \Z: k > 0$ and $i \in \Z$ such that:

$(1): \quad k$ is the smallest such that $\map {\rho^k} i = i$
$(2): \quad \rho$ fixes each $j$ not in $\set {i, \map \rho i, \ldots, \map {\rho^{k - 1} } i}$.

Subcategories

This category has the following 2 subcategories, out of 2 total.