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?