Continued fractions and Catalan problems

Thumbnail Image

Date

Authors

Journal Title

Journal ISSN

Volume Title

Publisher

Abstract

Description

We find a generating function expressed as a continued fraction that enumerates ordered trees by the number of vertices at different levels. Several Catalan problems are mapped to an ordered-tree problem and their generating functions also expressed as a continued fraction. Among these problems is the enumeration of (132)-pattern avoiding permutations that have a given number of increasing patterns of length k. This extends and illuminates a result of Robertson, Wilf and Zeilberger for the case k=3.
9 pages, 1 figure

Keywords

Combinatorics, 05A; 05C30

Citation

URI

http://salesiana.dossiersoluciones.com/handle/123456789/58539

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0001091
 http://arxiv.org/abs/math/0001091

Collections

arXiv