Sturmian strings

A string is a sequence of letters which are the elements of a specified set called alphabet. At this point we can see letters generate the word, words generate the string obviously.Sturmian Strings are defined on binary alphabet which is called and size 2. string, which is difined on alphabet, can be Sturmian String if and only if is balanced and not ultimately periodic.A finite Sturmian string is any finite non-empty substring of an infinite Sturmian string. A Fibonacci string is a special case of a sturmian string that is well-known. Sturmian strings are related to straight lines.Set of all central words denote by PER and every Sturmian word is a substring of a word in PER. Hence the set PER is a kernel of the Sturmian words. At this point it can be make knowledge about combinational properties of the Sturmian strings by using the PER.In this thesis, it is worked on different ways for defined and explaining of Sturmian string.Key Words: Word, String, Sturmian, Fibonacci Strings