### DIMACS - RUTGERS EXPERIMENTAL MATHEMATICS SEMINAR

Sponsored by the Rutgers University Department of Mathematics and the

Center for Discrete Mathematics and Theoretical Computer Science (DIMACS)

**Co-organizers:**
**Brian Nakamura**, Rutgers University, bnaka {at} math [dot] rutgers [dot] edu
** Doron Zeilberger**, Rutgers University, zeilberg {at} math [dot] rutgers [dot] edu

Title: On Subsets of Ordered Trees Enumerated by a Subsequence of Fibonacci Numbers

Speaker: **Melkamu Zeleke**, William Paterson University

Date: Thursday, April 18, 2013 5:00pm

Location: Hill Center, Room 705, Rutgers University, Busch Campus, Piscataway, NJ

Abstract:

Herb Wilf and Andrew Odlyzko provided a bijection between fountains of coins and partitions of integers studied by Szekeres in connection with a combinatorial interpretation of Ramanujan's continued fraction. In this talk, I will provide a direct bijection between subsets of ordered trees where no two vertices at the same level have different parents (a.k.a. Skinny Trees) and ordered trees with height at most three (a.k.a. Emeric's Trees) thereby showing the number of contiguous stacking of coins in which there are n coins in the bottom row is equal to the number of directed column convex polyominoes with n cells. I will also discuss Shapiro's generating function identity related to these combinatorial objects.

See: http://www.math.rutgers.edu/~bnaka/expmath/