Definition:Cycle Type

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

From 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.