Some Studies On Christoffel Words

Sturmian sequences play an important role in discrete dynamical, and are alsoresearch objects in Combinatorics on Words. Christo?el words are ?nite versionof Sturmian sequences, therefore, the study of Christo?el words will contribute tostudying Sturmian sequence.In the introductory chapter, we give some related de?nitions, notation, ba-sic knowledge and relevant conclusions. Then, we introduce the de?nition ofChristo?el words and Christo?el morphisms; give a generating set of the monoidof Christo?el morphisms; prove that every Christo?el word can be expressed asthe product of two Christo?el words in a unique way; study and show the rela-tionship between Christo?el words and vertices of Christo?el tree, the relationshipbetween Christo?el words and a kind palindromic words, and the relation amongChristo?el words, the continued fraction expansion of the corresponding slopeand Stern-Brocot tree. At last, we introduce the Burrow-Wheeler transform andbalanced words. At the same time, we give some other properties of Christo?elwords, and a method of computing Christo?el words by periodic phenomena.