Geodesic
Local probabilities for random permutations without long cycles
The electronic journal of combinatorics, Tome 23 (2016) no. 1
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We explore the probability $\nu(n,r)$ that a permutation sampled from the symmetric group of order $n!$ uniformly at random has no cycles of length exceeding $r$, where $1\leq r\leq n$ and $n\to\infty$. Asymptotic formulas valid in specified regions for the ratio $n/r$ are obtained using the saddle-point method combined with ideas originated in analytic number theory.
DOI : 10.37236/4758
Classification : 60C05, 60F10, 05A16
Mots-clés : symmetric group, cycle structure, short cycles, saddle-point method

Eugenijus Manstavičius  1   ; Robertas Petuchovas  1

1 Vilnius University 
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     title = {Local probabilities for random permutations without long cycles},
     journal = {The electronic journal of combinatorics},
     year = {2016},
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     number = {1},
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Eugenijus Manstavičius; Robertas Petuchovas. Local probabilities for random permutations without long cycles. The electronic journal of combinatorics, Tome 23 (2016) no. 1. doi: 10.37236/4758

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