MAT 320 Introduction to Analysis Fall 1996
Week by Week
Week 1. Catalan numbers. The question was, given a five
numbers x,y,z,w,v,
and a binary operation + which is not necessarily
associative, how many different ways are there to +
them up (keeping the order fixed). E.g. (((x+y)+
z)+w)+v is one.
The answer, as calculated in class,
was 14. Fourteen is the 4th Catalan number, and
it turns out that if we had chosen n numbers
instead of 5, the answer would have been the (n-1)st
Catalan number.
How are these numbers defined, how can they be calculated
and why are they related to the non-associativity problem
we started with?