Ostrowski Numeration and the Local Period of Sturmian Words

TL;DR

This paper establishes a connection between the local period at position n in characteristic Sturmian words and the Ostrowski representation of n+1, providing a new way to analyze their structure.

Contribution

It introduces a novel relationship between local periods in Sturmian words and Ostrowski numeration, enhancing understanding of their combinatorial properties.

Findings

Local period at position n can be expressed via Ostrowski representation of n+1.

Provides a new method to analyze Sturmian words using number representations.

Establishes a link between combinatorics on words and number theory.

Abstract

We show that the local period at position n in a characteristic Sturmian word can be given in terms of the Ostrowski representation for n + 1.