Expansions in multiple bases over general alphabets
Yuru Zou, Vilmos Komornik, Jian Lu

TL;DR
This paper develops a comprehensive framework for expansions in multiple bases over general alphabets, extending existing theories and improving results on unique expansions.
Contribution
It introduces a unified alphabet-base system framework that encompasses previous models and extends Parry's lexicographic theory to this broader setting.
Findings
Unified framework for alphabet-base expansions
Extension of Parry's lexicographic theory
Generalization of results on unique expansions
Abstract
Expansions in non-integer bases have been extensively investigated since a pioneering work of R\'enyi. We introduce a more general framework of alphabet-base systems that also includes Pedicini's general alphabets and the multiple-base expansions of Neunh\"auserer and Li. We extend the Parry type lexicographic theory to this setup, and we improve and generalize various former results on unique expansions.
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Taxonomy
Topicssemigroups and automata theory · Mathematical Dynamics and Fractals · Advanced Algebra and Logic
