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Search: id:A113869
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| A113869 |
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Coefficients in asymptotic expansion of probability that a random pair of elements from the alternating group A_k generates all of A_k. |
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+0
5
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| 1, -1, -1, -4, -23, -171, -1542, -16241, -194973, -2622610, -39027573, -636225591, -11272598680, -215668335091, -4431191311809, -97316894892644, -2275184746472827, -56421527472282127, -1479397224086870294, -40897073524132164189, -1188896226524012279617
(list; graph; listen)
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OFFSET
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0,4
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REFERENCES
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L. Babai, The probability of generating the symmetric group, J. Combin. Theory (Ser. A) 52 (1989) 148-153.
J. Bovey and A. Williamson, The probability of generating the symmetric group, Bull. London Math. Soc. 10 (1978) 91-96.
J. D. Dixon, The probability of generating the symmetric group, Math. Z. 110 (1969) 199-205.
J. D. Dixon, Asymptotics of generating the symmetric and alternating groups, Electron. J. Combin., Item R56 of Volume 12(1), 2005.
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FORMULA
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The probability that a random pair of elements from the alternating group A_k generates all of A_k is P_k ~ 1-1/k-1/k^2-4/k^3-23/k^4-171/k^5-... = Sum_{n >= 0} a(n)/k^n.
Furthermore, P_k ~ 1 - Sum_{n >= 1} A003319(n)/[k]_n, where [k]_n = k(k-1)(k-2)...(k-n+1). Therefore for n >= 2, a(n) = - Sum_{i=1..n} A003319(i)*Stirling_2(n-1, i-1). - N. J. A. Sloane (njas(AT)research.att.com).
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CROSSREFS
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Cf. A003319, A113871, A114038.
Sequence in context: A111547 A158884 A053525 this_sequence A084357 A075729 A127131
Adjacent sequences: A113866 A113867 A113868 this_sequence A113870 A113871 A113872
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KEYWORD
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sign,nice
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com), Jan 26 2006
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