Palindromes and Sturmian words

An infinite word x over the alphabet A is Sturmian if and only if g(x)(n)= n + 1 for any integer n, where g(x)(n) is the number of distinct words of length n occurring in x. A palindrome is a word that can be read indistinctly from left to right or from right to left. We prove that x is Sturmian if and only if h(x)(n)= 1 + (n mod 2) for ally integer n, where h(x)(n) is the number of palindromes of length n occurring in x. An infinite word x over the alphabet A is generated by a morphism f if there exists a letter c is an element of A such that lim(n-->infinity) f(n)(c) = x. We prove the existence of a morphism that generates the palindromes of any infinite Sturmian word generated by a morphism. (C) 1999 Elsevier Science B.V. All rights reserved.