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arXiv · 1406.3081

Integer sequences and k-commuting permutations

Luis Manuel Rivera
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Abstract

Let $\beta$ be any permutation on $n$ symbols and let $c(k, \beta)$ be the number of permutations that $k$-commute with $\beta$. The cycle type of a permutation $\beta$ is a vector $(c_1, \dots, c_n)$ such that $\beta$ has exactly $c_i$ cycles of length $i$ in its disjoint cycle factorization. In this article we obtain formulas for $c(k, \beta)$, 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.

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Luis Manuel Rivera. 2014-06-11. Integer sequences and k-commuting permutations. https://arxiv.org/abs/1406.3081

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