Definition:Cycle Type

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

From Existence and Uniqueness of Cycle Decomposition, every element of $S_n$ may be uniquely expressed as a product of disjoint cycles, up to the order of factors.

Let $\pi, \rho \in S_n$.

Then $\pi$ and $\rho$ have the same cycle type if they have the same number of cycles of equal length.