A characterization of substitutive sequences using return words

TL;DR

This paper characterizes primitive substitutive sequences by establishing that their derived sequences form a finite set, providing a new way to identify and analyze such sequences.

Contribution

It introduces the concept of derived sequences and proves a bi-conditional characterization of primitive substitutive sequences.

Findings

Primitive substitutive sequences have finitely many derived sequences.

Derived sequences are a key tool for characterizing substitutive sequences.

The paper establishes a new criterion for identifying primitive substitutive sequences.

Abstract

We prove that a sequence is primitive substitutive if and only if the set of its derived sequences is finite; we defined these sequences here.