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arXiv · 1605.02690

Recent results on permutations without short cycles

Robertas Petuchovas
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Abstract

The density, denoted by $κ(n,r)$, of permutations having no cycles of length less than $r+1$ in a symmetric group $\mathrm{S}_n$ is explored. New asymptotic formulas for $κ(n,r)$ are obtained using the saddle-point method when $5\leq r< n$ and $n\to\infty$.

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Robertas Petuchovas. 2016-05-09. Recent results on permutations without short cycles. https://arxiv.org/abs/1605.02690

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