# Category:Examples of Cycle Notation

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This category contains examples of Cycle Notation.

The $k$-cycle $\rho$ is denoted:

- $\begin {pmatrix} i & \map \rho i & \ldots & \map {\rho^{k - 1} } i \end{pmatrix}$

From Existence and Uniqueness of Cycle Decomposition, all permutations can be defined as the product of disjoint cycles.

As Disjoint Permutations Commute, the order in which they are performed does not matter.

So, for a given permutation $\rho$, the **cycle notation** for $\rho$ consists of all the disjoint cycles into which $\rho$ can be decomposed, concatenated as a product.

It is conventional to omit $1$-cycles from the expression, and to write those cycles with lowest starting number first.

## Pages in category "Examples of Cycle Notation"

The following 3 pages are in this category, out of 3 total.