Recursive bijections for Catalan objects
Stefan Forcey, Mohammadmehdi Kafashan, Mehdi Maleki, Michael Strayer

TL;DR
This paper explores recursive and local bijections between different combinatorial structures counted by Catalan numbers, addressing questions posed by R. Stanley and providing insights into their relationships.
Contribution
It introduces new recursive and local bijections between Catalan-structured sets, enhancing understanding of their combinatorial correspondences.
Findings
Established recursive bijections between Catalan objects
Compared recursive and local bijection methods
Addressed open questions from R. Stanley's textbook
Abstract
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.
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Taxonomy
TopicsAdvanced Combinatorial Mathematics · semigroups and automata theory · Advanced Mathematical Identities
