Combinatorics, Week 4
February 15, 2017

For this meeting, we will work together some counting problems involving non-intersecting arcs, and continue our study of examples that yield Catalan numbers.

I have prepared some hand notes on various approaches to counting non-intersecting arcs:

• Week-4-Combinatorics

This Wikipedia page is a good introduction to Catalan numbers:

• Catalan number

One can look up 1, 1, 2, 5, 14, 42 or 3, 14, 40, 90 online:

• The On-Line Encyclopedia of Integer Sequences

This book is dedicated to Catalan numbers:

• 2015 Roman - An Introduction to Catalan Numbers

• 1983 Pólya, Tarjan, Woods - Notes on Elementary Combinatorics

pp 25-31 discuss dissecting an n-gon into triangles.

• 2011 Camina, Lewis - An introduction to enumeration

pp 198-202 consider Catalan numbers.

• 2007 Aigner - A Course in Enumeration

This is intended as a text for graduate students, yet it is quite readable. One may prefer its mature style.

pp 101-102 and 202-203 briefly consider Catalan numbers.