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Permutation Patterns and Continued Fractions
Aaron Robertson, Herbert S. Wilf, Doron Zeilberger
Source abstract
We find, in the form of a continued fraction, the generating function for the number of -avoiding permutations that have a given number of patterns, and show how to extend this to permutations that have exactly one pattern. We also find some properties of the continued fraction, which is similar to, though more general than, those that were studied by Ramanujan.
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