Geodesic
Permutation patterns and continued fractions
The electronic journal of combinatorics, Tome 6 (1999)
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We find, in the form of a continued fraction, the generating function for the number of $(132)$-avoiding permutations that have a given number of $(123)$ patterns, and show how to extend this to permutations that have exactly one $(132)$ pattern. We also find some properties of the continued fraction, which is similar to, though more general than, those that were studied by Ramanujan.
DOI : 10.37236/1470
Classification : 05A15
Mots-clés : pattern, perturbation 
@article{10_37236_1470,
     author = {Aaron Robertson and Herbert S. Wilf and Doron Zeilberger},
     title = {Permutation patterns and continued fractions},
     journal = {The electronic journal of combinatorics},
     year = {1999},
     volume = {6},
     doi = {10.37236/1470},
     zbl = {0937.05004},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/1470/}
}
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AU  - Doron Zeilberger
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%A Aaron Robertson
%A Herbert S. Wilf
%A Doron Zeilberger
%T Permutation patterns and continued fractions
%J The electronic journal of combinatorics
%D 1999
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%U http://geodesic.mathdoc.fr/articles/10.37236/1470/
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Aaron Robertson; Herbert S. Wilf; Doron Zeilberger. Permutation patterns and continued fractions. The electronic journal of combinatorics, Tome 6 (1999). doi: 10.37236/1470

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