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The Expected order of a Random Permutation
Author(s) -
Goh William M. Y.,
Schmutz Eric
Publication year - 1991
Publication title -
bulletin of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.396
H-Index - 48
eISSN - 1469-2120
pISSN - 0024-6093
DOI - 10.1112/blms/23.1.34
Subject(s) - mathematics , random permutation , permutation (music) , combinatorics , order (exchange) , permutation group , symmetric group , cyclic permutation , partial permutation , parity of a permutation , binary logarithm , discrete mathematics , physics , finance , acoustics , economics
Let μ n be the expected order of a random permutation, that is, the arithmetic mean of the orders of the elements in the symmetric group S n . We prove that log μ n ñ c √( n /log n ) as n → ∞, where c = 2( 2 ∫ 0 ∞ log log ( e 1 ‐ e ‐ t) d t ).
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