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Horizons in Combinatorics/16th Shanks Lecture Series
May 21-24, 2001
Vanderbilt University
Nashville, TN, USA

Organizers
Paul Edelman, Mark Ellingham, Jonathan Farley, Mike Plummer, Jerry Spinrad

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Results for Generalized Catalan Problems
by
Naiomi T. Cameron
Howard University

Paths in the first quadrant starting at the origin with step set { (1, 1), (1, -2) } are counted by ternary numbers, [ 1/(2n+1)](3n || n), which can be considered a generalization of the Catalan numbers. The relationship between the Motzkin and Catalan numbers is extended to this and other settings, with combinatorial proofs provided. An approach to calculating the area bounded by these paths is introduced.

Date received: April 20, 2001

Copyright © 2001 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Mathematical Conference Abstracts. Document # cags-68.