Keywords: combinatorics

Prerequisites: 01018: Discrete Mathematics 2

Combinatorics is the art of counting things. Pólya’s Enumeration Theorem is a powerful theorem for counting many types of recursively defined objects. A prime example, lending the suggested title to this project, is how many circular neclaces can you make with, say, 10 beads on it, each one red, green or blue? Of course, two neclaces are considered the same if I can roll the pearls around on the string on one and obtain the other, or if I can turn over the necklace and do the same.

In this project, you will become familiar with and prove Pólya’s Enumeration Theorem, and you will apply it to several concrete counting problems.