Abstract
We introduce and study k-commuting permutations. One of our main results is a characterization of permutations that k-commute with a given permutation. Using this characterization, we obtain formulas for the number of permutations that k-commute with a permutation beta , for some cycle types of beta . Our enumerative results are related with integer sequences in “The On-line Encyclopedia of Integer Sequences”, and in some cases provide new interpretations for such sequences.
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