Section 3.1 Classification Problems
The first unit of this course studied the question of enumeration: How many ____ are there? There are many ways to investigate enumeration problems, including such techniques as generating functions, asymptotic analysis, Polya enumeration, etc. The two techniques we focused on were bijections and recursions, which are fundamental to enumeration.
In our next unit, we will focus on the question of classification: Which objects have ____ property? Classification problems have a much different feel than enumeration problems. In particular, while we will sometimes engage in counting problems, when studying classification problems we are much more interested in structure and quality rather than quantity. We will begin by studying classification problems for trees and graphs, and we will end this unit by considering a classification problem involving permutations.
