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Abstract: This paper is concerned with palindromes occurring in characteristic Sturmianwords $c \alpha$ of slope $\alpha$, where $\alpha \in 0,1$ is an irrational.As $c \alpha$ is a uniformly recurrent infinite word, any palindromic factorof $c \alpha$ occurs infinitely many times in $c \alpha$ with bounded gaps. Ouraim is to completely describe where palindromes occur in $c \alpha$. Inparticular, given any palindromic factor $u$ of $c \alpha$, we shall establisha decomposition of $c \alpha$ with respect to the occurrences of $u$. Such adecomposition shows precisely where $u$ occurs in $c \alpha$, and this isdirectly related to the continued fraction expansion of $\alpha$.



Author: Amy Glen

Source: https://arxiv.org/



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