Blocks in cycles and k-commuting permutations
Blocks in cycles and k-commuting permutations
Let $k$ be a nonnegative integer, and let $\alpha$ and $\beta$ be two permutations of $n$ symbols. We say that $\alpha$ and $\beta$ $k$-commute if $H(\alpha\beta, \beta\alpha)=k$, where $H$ denotes the Hamming metric between permutations. In this paper, we consider the problem of finding the permutations that $k$-commute with a …