String attractors of some simple-Parry automatic sequences

TL;DR

This paper investigates string attractors for prefixes of infinite words related to simple Parry numbers, extending previous work on k-bonacci and Fibonacci words using numeration systems derived from morphisms.

Contribution

It provides a new characterization of string attractors for a class of infinite words associated with simple Parry numbers, generalizing prior results on k-bonacci and Fibonacci words.

Findings

String attractors are explicitly described for prefixes of these infinite words.

The description involves numeration systems linked to the morphisms defining the words.

Extends previous work to a broader class of infinite words.

Abstract

Firstly studied by Kempa and Prezza in 2018 as the cement of text compression algorithms, string attractors have become a compelling object of theoretical research within the community of combinatorics on words. In this context, they have been studied for several families of finite and infinite words. In this paper, we obtain string attractors of prefixes of particular infinite words generalizing k-bonacci words (including the famous Fibonacci word) and related to simple Parry numbers. In fact, our description involves the numeration systems classically derived from the considered morphisms. This extends our previous work published in the international conference WORDS 2023.