Permutation Patterns and Continued Fractions

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. 

• Type: Journal
• Year: 1999
• Where: COMBINATORICS
• Authors: Aaron Robertson, Herbert S. Wilf, Doron Zeilberger
• Keywords: COMBINATORICS 1999, Continued Fraction, Generating Function, Permutations