arXiv:math/9906154 Abstract

arXiv:math/9906154 [math.CO]Abstract References Reviews Resources

Patterns and Fractions

Aaron Robertson, Herb Wilf, Doron Zeilberger

Published 1999-06-23Version 1

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.

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

Categories: math.CO

Subjects: 05A15

Keywords: continued fraction, permutations, generating function

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