Continued fractions and Catalan problems
组合数学
2007-05-23 v1
摘要
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.
引用
@article{arxiv.math/0001091,
title = {Continued fractions and Catalan problems},
author = {Mahendra Jani and Robert G. Rieper},
journal= {arXiv preprint arXiv:math/0001091},
year = {2007}
}
备注
9 pages, 1 figure