Definition:Cycle Type
From ProofWiki
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.
Sources
- John F. Humphreys: A Course in Group Theory (1996): $\S 9$: Proposition $9.20$: Remark
