Patterns and Fractions

1999/06/23 by Aaron Robertson, Robertson, Aaron, Herb Wilf +3
Mathematics · #05A15 #Combinatorics (math.CO) #FOS: Mathematics #math.CO #msc:05A15

paper · pdf · doi:10.48550/arxiv.math/9906154

This paper supercedes "The number of permutations with a prescribed number of 132 and 123 patterns" (math.CO/9903170)

arxiv created 1999/06/23 · arxiv updated 2009/11/30

Abstract

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 find some properties of the continued fraction, which is similar to, though more general than, those that were studied by Ramanujan.

Related

• Permutations Containing and Avoiding 123 and 132 Patterns
• Continued fractions and Catalan problems
• Permutations with restricted patterns and Dyck paths
• Permutations Which Avoid 1243 and 2143, Continued Fractions, and Chebyshev Polynomials
• Continued fractions and generalized patterns