Blocks in cycles and k-commuting permutations

Springerplus. 2016 Nov 10;5(1):1949. doi: 10.1186/s40064-016-3638-7. eCollection 2016.


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 [Formula: see text], for some cycle types of [Formula: see text]. 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.

Keywords: Commutation relation; Enumeration; Hamming metric; Symmetric group.