Occurrences of palindromes in characteristic Sturmian words

Abstract

This paper is concerned with palindromes occurring in characteristic Sturmian words c α of slope α , where α ∈ ( 0 , 1 ) is an irrational. As c α is a uniformly recurrent infinite word, any (palindromic) factor of c α occurs infinitely many times in c α with bounded gaps. Our aim is to completely describe where palindromes occur in c α . In particular, given any palindromic factor u of c α , we shall establish a decomposition of c α with respect to the occurrences of u. Such a decomposition shows precisely where u occurs in c α , and this is directly related to the continued fraction expansion of α .