Geodesic
The enumeration of simple permutations
Journal of integer sequences, Tome 6 (2003) no. 4
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 
@article{JIS_2003__6_4_a5,
     author = {Albert,  M.H. and Atkinson,  M.D. and Klazar,  M.},
     title = {The enumeration of simple permutations},
     journal = {Journal of integer sequences},
     year = {2003},
     volume = {6},
     number = {4},
     zbl = {1065.05001},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JIS_2003__6_4_a5/}
}
TY  - JOUR
AU  - Albert,  M.H.
AU  - Atkinson,  M.D.
AU  - Klazar,  M.
TI  - The enumeration of simple permutations
JO  - Journal of integer sequences
PY  - 2003
VL  - 6
IS  - 4
UR  - http://geodesic.mathdoc.fr/item/JIS_2003__6_4_a5/
LA  - en
ID  - JIS_2003__6_4_a5
ER  - 
%0 Journal Article
%A Albert,  M.H.
%A Atkinson,  M.D.
%A Klazar,  M.
%T The enumeration of simple permutations
%J Journal of integer sequences
%D 2003
%V 6
%N 4
%U http://geodesic.mathdoc.fr/item/JIS_2003__6_4_a5/
%G en
%F JIS_2003__6_4_a5
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/