Dixon, J. D. The probability of generating the symmetric group. (English) Zbl 0176.29901 Math. Z. 110, 199-205 (1969). Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page Cited in 11 ReviewsCited in 98 Documents Keywords:group theory Citations:JFM 24.0134.02; JFM 14.0090.01; Zbl 0189.31302 PDFBibTeX XMLCite \textit{J. D. Dixon}, Math. Z. 110, 199--205 (1969; Zbl 0176.29901) Full Text: DOI EuDML Online Encyclopedia of Integer Sequences: Number of connected permutations of [1..n] (those not fixing [1..j] for 0 < j < n). Also called indecomposable permutations, or irreducible permutations. a(n) = n! times probability that an ordered pair of elements of S_n chosen at random (with replacement) generate S_n. Number of ordered pairs (a,b) of elements of the symmetric group S_n such that the pair a,b generates S_n. Coefficients in asymptotic expansion of probability that a random pair of elements from the alternating group A_k generates all of A_k. References: [1] Erdös, P., and P. Turán: On some problems of a statistical group-theory. II. Acta Math. Acad. Sci. Hung.18, 151-163 (1967). · Zbl 0189.31302 · doi:10.1007/BF02020968 [2] Hardy, G. H., and E. M. Wright: An introduction to the theory of numbers. Oxford: Clarendon Press 1962. · Zbl 0020.29201 [3] Netto, E.: The theory of substitutions (reprint). New York: Chelsea 1964. (This translation was first published in 1892). [4] Wielandt, H.: Finite permutation groups. New York: Academic Press 1964. · Zbl 0138.02501 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.