A Structure Of Sturmian Sequence About Its Factors

In this thesis we mainly study the structure of the factors of Sturmian sequences. Given be a Sturmian sequence U and a factor w of U, let us delete in turn all w's in U. We then get a new sequence, which is called a remaining sequence. According to different factors, we give a classification for the remaining sequences. Finally, we discuss the remaining sequences under bijection: Most of them can be changed into a Sturmian sequence by bijection, while a few of them can't turn into a Sturmian sequence by bijection. The main content of this is summarized as follows:In the first chapter, we briefly introduce the evolution on the Sturmian sequences and combinatorics on words, as well as some topics about Sturmian sequences in recent years.In the second chapter, we introduce the preliminaries of Sturmian sequences and its other definitions, such as Balanced sequences, Cutting sequences and Rotation sequences, etc.In the last chapter, the main reseach is as follows: Firstly, since a Sturmian sequence is an aperiodic sequences with minimal language complexity, we can make some reasonable constriction for them, that is, let the Sturmian sequences be standard and with its slope less than 1. Secondly, by the exact increase of lengths of the standard words we can restrict the length of the selected factor between the lengths of two consecutive standard words. Thirdly, according to relations between the selected factor and some special factors, we study the remaining sequences, and give a classification of the factors of remaining sequences. Finally, from the properties of the original sequences, we obtain the conclusion: Most of them can be changed into a Sturmian sequence by bijection, while a few of them can't turn into a Sturmian by bijection.