Patterns and Fractions

Details Patterns and Fractions Patterns and Fractions

1999-06-23

arxiv.org/abs/math/9906154v1

Mathematics

Combinatorics

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

Scientific paper

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.

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