Three tutorial lectures on entropy and counting

TL;DR

This paper provides an accessible explanation of entropy for discrete variables, illustrating its use in combinatorial enumeration and discussing open questions in the field.

Contribution

It introduces entropy concepts with examples and explores their application in counting problems, offering insights for both beginners and researchers.

Findings

Entropy helps in counting and enumeration tasks.

Basic properties of entropy are derived and explained.

Open questions in entropy and combinatorics are discussed.

Abstract

We explain the notion of the {\em entropy} of a discrete random variable, and derive some of its basic properties. We then show through examples how entropy can be useful as a combinatorial enumeration tool. We end with a few open questions.