+ Catalan Numbers Noor Doukmak April 25, 2013
Dec 15, 2015
+Outline
Introduction
Descriptions
Generating Functions, closed-form formula
Asymptotics
Formal Grammar
Continued Fractions
Dyck Triangle
+Introduction
Belgian mathematician Eugène Charles Catalan (1814–1894)
How to bracket n+1 items using n pairs of brackets?
Cannot close a bracket without opening the corresponding one
+Formal grammar
It is helpful to define production rules for words that make up the Dyck language.
Every word is either the empty word, or Dyck word sandwiched between a and b + Dyck
word
We represent this as: