INTEGER SEQUENCES AND K-COMMUTING PERMUTATIONS

摘要

Let be any permutation on n symbols, and let c(k, ) be the number of permutations that k-commute with . The cycle type of a permutation is a vector (c1, . . . , cn) such that has exactly ci cycles of length i in its disjoint cycle factorization. In this article we obtain formulas for c(k, ), for some cycle types. We also express these formulas in terms of integer sequences as given in “The On-line Encyclopedia of Integer Sequences” (OEIS). For some of these sequences, we obtain either new interpretations or relationships with sequences in the OEIS database.