Occurrences of palindromes in characteristic Sturmian words

Abstract

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

17 pages

References in corpus (1)

• Conjugates of characteristic Sturmian words generated by morphisms

Cited by in corpus (5)

• Sturmian numeration systems and decompositions to palindromes
• Local symmetry dynamics in one-dimensional aperiodic lattices
• Gap Sequence of Factors of Fibonacci Sequence
• Powers in a class of A-strict standard episturmian words
• Palindromes In Sturmian Strings