Christoffel Words and Associated Algorithms

This thesis discusses Christoffel words, a subset of the free monoid on two letters, and algorithms which can produce them. It covers Christoffel morphisms, standard factorizations, the Burrows-Wheeler matrix, and continued fractions, and the four algorithms included serve as a way to demonstrate these ideas in relation to Christoffel words. Code for these algorithms is included which can be used in the GAP programming language. The thesis concludes with an examination of some modern and ancient calendar systems and their relationship to Christoffel words.