In group theory a transposition is a permutation that exchanges two elements and leaves all others fixed.
For $n \in \mathbb{N}$ and $1 \leq i \neq j \leq n$, the transposition of $i$ with $j$ among $\{1,\cdots, n\}$ is the permutation
Transpositions are generators for the symmetric group, exhibiting it as a finitely generated group.
In fact already just the adjacent transpositions $t_{i , i+1}$ for $1 \leq i \leq n$ generate the symmetric group, see at Kendall tau distance.
Created on April 17, 2021 at 15:49:29. See the history of this page for a list of all contributions to it.