What Is Enumeration?

Abstract

Enumerative mathematics (also commonly called combinatorics) is concerned with arrangements of a given set of objects according to precise rules. The aim is to count the number of possible arrangements by recognizing and exploiting the patterns that make them up. Sometimes the result is an explicit formula for the count; sometimes different patterns of the same arrangement will result in different expressions which are thus equal. As we shall see, many different branches of mathematics provide strikingly different ways in which we can count. This book explores some of these.

We begin our study of such patterns with some simple-looking principles – self-evident really. They hide very sophisticated and powerful enumerative techniques.