For any integers 
with
 |
the proportion of permutations in the symmetric group 
whose cyclic decompositions contain no cycles of lengths 
, 
, ..., 
is at most
 |
(Erdős and Turán 1967, Dixon 1969).
Erdős-Turán Theorem
See also
Permutation Cycle, Symmetric GroupExplore with Wolfram|Alpha
References
Dixon, J. D. "The Probability of Generating the Symmetric Group." Math. Z. 110, 199-205, 1969.Erdős, P. and Turán, P. "On Some Problems in Statistical Group Theory. II." Acta Math. Acad. Sci. Hung. 18, 151-163, 1967.Referenced on Wolfram|Alpha
Erdős-Turán TheoremCite this as:
Weisstein, Eric W. "Erdős-Turán Theorem." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/Erdos-TuranTheorem.html