C3 - cycle

(a_{1}, a_{2}, \dots, a_{m}) (k) = {\begin{cases} a_{i + 1} & if k = a_{i}, 1 \leq a_{i} \leq m, \\ a_{1} & if k = a_{m}, \\ k & if k \notin {a_{1}, a_{2,} \dots, m} . \end{cases}

[\begin{matrix} a_{1} & a_{2} & \dots & a_{i} & \dots & a_{m - 1} & a_{m} \\ a_{2} & a_{3} & \dots & a_{i + 1} & \dots & a_{m} & a_{1} \end{matrix}]