Kenyon Theorem Revisited

2025/08/26 by Głąb, Szymon, Kula, Mateusz · 1 citation
#40A #FOS: Mathematics #General Topology (math.GN)

paper · doi:10.48550/arxiv.2508.19454

Abstract

We study sets E(Σ,q)=\∑_i=1^∞ σ_iqⁱ\colon(σ_i)∈Σ^{\mathbb N}\ for a finite set Σ⊂ \mathbb R and q∈(0,1). Under the assumption q|Σ|=1 we prove several new equivalent conditions for E(Σ,q) to contain an interval. We give a full characterization, if additionally |Σ| is prime.

Citations

• Recent progress on Bernoulli convolutions
• Projecting the one-dimensional Sierpinski gasket

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• On a new condition implying that an achievement set is a Cantorval and its applications

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