> [!NOTE] Definition (Cycle Notation) > Let $n\in\mathbb{N}^{+}$ and $\rho:\mathbb{N}^{+}_{\leq n}\to \mathbb{N}^{+}_{\leq n}$ be a [[Cyclic Permutation of n Letters|cyclic permutation]] of length $k.$ Then $\rho$ is denoted $(i, \rho(i),\rho^{2}(i),\dots,\rho^{k-1}(i))$ > [!Example] Example > The permutation expressed in [[Two-Row Notation|two-row notation]] as $\begin{pmatrix}1&2&3&4&5\\4&2&3&5&1\end{pmatrix}$can be expressed in cycle notation as $(1,4,5).$