Recursive bijections for Catalan objects
  In this note we introduce several instructive examples of bijections found between several different combinatorially defined sequences of sets. 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. 
Stefan Forcey, Mohammadmehdi Kafashan, Mehdi Maleki, Michael Strayer
math.CO