On the number of unique expansions in non-integer bases

DOI10.1016/J.TOPOL.2008.09.001zbMath1160.11002arXiv0805.2047OpenAlexW2063330500MaRDI QIDQ1004051

Martijn de Vries

Publication date: 2 March 2009

Published in: Topology and its Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0805.2047

zbMATH Keywords

Thue-Morse sequencegreedy expansionquasi-greedy expansionunique expansionunivoque sequenceunivoque number

Mathematics Subject Classification ID

Special sequences and polynomials (11B83) Radix representation; digital problems (11A63)

Related Items (8)

Hausdorff dimension of univoque sets and devil's staircase ⋮ Univoque bases and Hausdorff dimension ⋮ Critical bases for ternary alphabets ⋮ Generalized golden ratios of ternary alphabets ⋮ Expansions in multiple bases ⋮ Unique expansions of real numbers ⋮ Hausdorff dimension of frequency sets of univoque sequences ⋮ Expansions of generalized Thue-Morse numbers

Cites Work

• Cantor type functions in non-integer bases
• On the topological structure of univoque sets
• Invariant densities for random \(\beta\)-expansions
• Unique expansions of real numbers
• On the uniqueness of the expansions \(1=\sum q^{-n_i}\)
• Representations for real numbers and their ergodic properties
• On theβ-expansions of real numbers
• Unique Developments in Non-Integer Bases
• Almost Every Number Has a Continuum of b-Expansions
• Characterization of the unique expansions $1=\sum^{\infty}_{i=1}q^{-n_ i}$ and related problems
• Unique representations of real numbers in non-integer bases
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