A040175 a(n) = n! times probability that an ordered pair of elements of S_n chosen at random (with replacement) generate S_n.
3, 9, 57, 318, 3090, 24666, 234879, 2381481, 26777922, 324421053, 4265966685
Offset: 3
Examples
Probabilities for n=1,2,3,... are 1, 3/4, 1/2, 3/8, 19/40, ...
References
- J. D. Dixon, Problem 923 (BCC20.17), Indecomposable permutations and transitive groups, in Research Problems from the 20th British Combinatorial Conference, Discrete Math., 308 (2008), 621-630.
Links
- L. Babai, The probability of generating the symmetric group, J. Combin. Theory, A52 (1989), 148-153.
- J. D. Dixon, The probability of generating the symmetric group, Math. Z. 110 (1969) 199-205.
- T. Łuczak and L. Pyber, On random generation of the symmetric group, Combin. Probab. Comput., 2 (1993), 505-512.
- A. Maroti and C. M. Tamburini, Bounds for the probability of generating the symmetric and alternating groups, Arch. Math. (Basel), 96 (2011), 115-121.
Formula
a(n) = A071605(n)/n!.
Extensions
Edited by Max Alekseyev, Jan 28 2012
a(10)-a(13) from Stephen A. Silver, Feb 21 2013
Comments