Sponsored by the Rutgers University Department of Mathematics and the
Center for Discrete Mathematics and Theoretical Computer Science (DIMACS)
Title: Continued Fractions and Catalan Problems
Speaker: Mahendra Jani, William Patterson University
Date: March 3, 2005 4:30-5:30pm
Location: Hill Center, Room 705, Rutgers University, Busch Campus, Piscataway, NJ
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 are 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.
(Joint work with Dr. Robert G. Rieper)