SOME COMBINATORIAL PROPERTIES OF STURMIAN WORDS

In this paper we give a characterization of finite Sturmian words, by palindrome words, which generalizes a property of the Fibonacci words. We prove that the set St of finite Sturmian words coincides with the set of the factors of all the words w such that w=AB=Cxy with A,B,C palindromes, x,y is an element of{a,b}, b) and x not equal y. Moreover, using this result we prove that St is equal to the set of the factors of all words w having two periods p and q which are coprimes and such that Absolute value of w greater than or equal to p+q-2. Several other combinatorial properties concerning special and bispecial elements of Sr are shown. As a consequence we give a new, and purely combinatorial, proof of the enumeration formula of St.