Occurrences of palindromes in characteristic Sturmian words

Details Occurrences of palindromes in characteristic Sturmian words Occurrences of palindromes in characteristic Sturmian words

2007-08-31

arxiv.org/abs/0708.4389v1

Theoretical Computer Science 352 (2006) 31-46

Mathematics

Combinatorics

17 pages

Scientific paper

10.1016/j.tcs.2005.09.075

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 $\alpha$.

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