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**
Recursive Bijections for Catalan Objects
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Stefan Forcey

Department of Mathematics

The University of Akron

Akron, OH 44325-4002

USA

Mohammadmehdi Kafashan and Mehdi Maleki

Department of Electrical Engineering

The University of Akron

Akron, OH 44325-4002

USA

Michael Strayer

Department of Mathematics

The University of Akron

Akron, OH 44325-4002

USA

**Abstract:**

In this note we introduce several instructive examples of bijections
found between several different combinatorially defined sequences
ofsets. Each sequence has cardinalities given by the Catalan numbers.
Our results answer some questions posed by R. Stanley in the addendum
to his textbook. We actually discuss two types of bijection, one
defined recursively and the other defined in a more local, relative,
fashion. It is interesting to compare the results of the two.

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(Concerned with sequence
A000108.)

Received December 1 2012;
revised version received February 24 2013; May 2 2013.
Published in *Journal of Integer Sequences*, May 9 2013.

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