# Conjugates of characteristic Sturmian words generated by morphisms - Mathematics > Combinatorics

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Abstract: This article is concerned with characteristic Sturmian words of slope$\alpha$ and $1-\alpha$ denoted by $c \alpha$ and $c {1-\alpha}$respectively, where $\alpha \in 0,1$ is an irrational number such that$\alpha = 0;1+d 1,\bar{d 2,

.,d n}$ with $d n \geq d 1 \geq 1$. It is knownthat both $c \alpha$ and $c {1-\alpha}$ are fixed points of non-trivialstandard morphisms $\sigma$ and $\hat{\sigma}$, respectively, if and only if$\alpha$ has a continued fraction expansion as above. Accordingly, such words$c \alpha$ and $c {1-\alpha}$ are generated by the respective morphisms$\sigma$ and $\hat{\sigma}$. For the particular case when $\alpha =0;2,\bar{r}$ $r\geq1$, we give a decomposition of each conjugate of$c \alpha$ and hence $c {1-\alpha}$ into generalized adjoining singularwords, by considering conjugates of powers of the standard morphism $\sigma$ bywhich it is generated. This extends a recent result of Lev\-{e} and S\ee boldon conjugates of the infinite Fibonacci word.

Author: ** Amy Glen**

Source: https://arxiv.org/