Fixed points of morphisms among binary generalized pseudostandard words

TL;DR

This paper introduces a class of fixed points of primitive morphisms within aperiodic binary generalized pseudostandard words, proposing it may encompass all such fixed points outside standard Sturmian words.

Contribution

The paper defines a new class of fixed points of primitive morphisms in aperiodic binary generalized pseudostandard words and conjectures its completeness.

Findings

Proposed a new class of fixed points in binary generalized pseudostandard words.

Conjectured this class includes all non-Sturmian fixed points of primitive morphisms.

Provided theoretical framework for future verification of the conjecture.

Abstract

We introduce a class of fixed points of primitive morphisms among aperiodic binary generalized pseudostandard words. We conjecture that this class contains all fixed points of primitive morphisms among aperiodic binary generalized pseudostandard words that are not standard Sturmian words.