Jump to navigation Jump to search
Let $S_n$ denote the symmetric group on $n$ letters.
Let $\pi, \rho \in S_n$ both be permutations on $S_n$.
Then $\pi$ and $\rho$ are disjoint if and only if:
- $(1): \quad i \notin \Fix \pi \implies i \in \Fix \rho$
- $(2): \quad i \notin \Fix \rho \implies i \in \Fix \pi$
We may say that:
- $\pi$ is disjoint from $\rho$
- $\rho$ is disjoint from $\pi$
- $\pi$ and $\rho$ are (mutually) disjoint.