Binary trees using the bookshelf and baseball constructions

TL;DR

This paper explores various combinatorial sets with Catalan numbers using novel 'bookshelf' and 'baseball' constructions, providing an accessible exposition of known bijections without requiring prior knowledge.

Contribution

It introduces new perspectives on Catalan objects through the 'bookshelf' and 'baseball' constructions, presenting bijections in an accessible manner.

Findings

Provides clear descriptions of Catalan sets and bijections

Introduces 'bookshelf' and 'baseball' constructions as new conceptual tools

Serves as an educational resource for understanding Catalan combinatorics

Abstract

This is a largely expository paper in which we discuss various sets having a Catalan number of objects and some well-known bijections between these sets presented in a new and hopefully interesting way. We call these concepts "bookshelf" and "baseball" constructions. No knowledge of these topics is assumed. These are the final student papers for a course at Brandeis University.