Bases which admit exactly two expansions

2022/01/13 by Yi Cai, Cai, Yi, Wenxia Li +1
Computer Science · Mathematics · #Advanced Topology and Set Theory #FOS: Mathematics #Limits and Structures in Graph Theory #Number Theory (math.NT) #semigroups and automata theory

paper · pdf · doi:10.48550/arxiv.2201.04776

openalex publication_date 2022/01/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

For a positive integer m let Ω_m=\0,1, ⋯ , m\ and \mathcal B₂(m)=amp; \q∈(1,m+1]: ∃ x∈ [0, m/(q-1)] has exactly .
amp;. two different q-expansions w.r.t. Ω_m \. Sidorov \citeS firstly studied the set \mathcal B₂(1) and raised some questions. Komornik and Kong \citeKK further studied the set \mathcal B₂(1) and answered partial Sidorov's questions. In the present paper, we consider the set \mathcal B₂(m) for general positive integer m and generalise the results obtained by Komornik and Kong.

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