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Search: id:A040175
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| A040175 |
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For n != 2, n! times probability that an ordered pair of elements of S_n chosen at random (with replacement) generate S_n (a(2)=3/2, which is here replaced by 1 since all entries must be integers). |
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+0
5
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OFFSET
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1,3
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REFERENCES
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J. D. Dixon, The probability of generating the symmetric group, Math. Z. 110 (1969) 199-205.
J. D. Dixon, Problem 923 (BCC20.17), Indecomposable permutations and transitive groups, in Research Problems from the 20th Britsh Combinatorial Conference, Discrete Math., 308 (2008), 621-630.
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EXAMPLE
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Probabilities for n=1,2,3,... are 1, 3/4, 1/2, 3/8, 19/40, ...
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CROSSREFS
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For n != 2, a(n) = A071605(n)/n!.
Probability is A040173/A040174 = A040175/n!.
Cf. A135474.
Sequence in context: A032179 A075979 A128681 this_sequence A105466 A018504 A018513
Adjacent sequences: A040172 A040173 A040174 this_sequence A040176 A040177 A040178
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KEYWORD
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nonn,more,nice
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AUTHOR
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Dan Hoey (Hoey(AT)aic.nrl.navy.mil)
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