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arXiv · 1710.11553

Sturmian numeration systems and decompositions to palindromes

Anna Frid
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Abstract

We extend the classical Ostrowski numeration systems, closely related to Sturmian words, by allowing a wider range of coefficients, so that possible representations of a number $n$ better reflect the structure of the associated Sturmian word. In particular, this extended numeration system helps to catch occurrences of palindromes in a characteristic Sturmian word and thus to prove for Sturmian words the following conjecture stated in 2013 by Puzynina, Zamboni and the author: If a word is not periodic, then for every $Q>0$ it has a prefix which cannot be decomposed to a concatenation of at most $Q$ palindromes.

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Anna Frid. 2017-11-02. Sturmian numeration systems and decompositions to palindromes. https://doi.org/10.1016/j.ejc.2018.04.003

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