Geodesic
The enumeration of simple permutations
Journal of integer sequences, Tome 6 (2003) no. 4.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: A simple permutation is one which maps no proper non-singleton interval onto an interval. We consider the enumeration of simple permutations from several aspects. Our results include a straightforward relationship between the ordinary generating function for simple permutations and that for all permutations, that the coefficients of this series are not $P$-recursive, an asymptotic expansion for these coefficients, and a number of congruence results for the coefficients of the functional inverse of the ordinary generating function for all permutations.
Classification : 05A05, 05A15, 05A16, 11A07
Keywords: permutation, P -recursiveness, asymptotic enumeration 
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     author = {Albert, M.H. and Atkinson, M.D. and Klazar, M.},
     title = {The enumeration of simple permutations},
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     number = {4},
     year = {2003},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JIS_2003__6_4_a5/}
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Albert, M.H.; Atkinson, M.D.; Klazar, M. The enumeration of simple permutations. Journal of integer sequences, Tome 6 (2003) no. 4. http://geodesic.mathdoc.fr/item/JIS_2003__6_4_a5/