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- W2969055364 abstract "Univoque numbers are real numbers $lambda > 1$ such that the number 1 admits a unique expansion in base $lambda$, i.e., a unique expansion $1 = sum_{j geq 0} a_j lambda^{-(j+1)}$, with $a_j in {0, 1, ..., lceil lambda rceil -1}$ for every $j geq 0$. A variation of this definition was studied in 2002 by Komornik and Loreti, together with sequences called {em admissible sequences}. We show how a 1983 study of the first author gives both a result of Komornik and Loreti on the smallest admissible sequence on the set ${0, 1, >..., b}$, and a result of de Vries and Komornik (2007) on the smallest univoque number belonging to the interval $(b, b+1)$, where $b$ is any positive integer. We also prove that this last number is transcendental. An avatar of the Thue-Morse sequence, namely the fixed point beginning in 3 of the morphism $3 to 31$, $2 to 30$, $1 to 03$, $0 to 02$, occurs in a universal manner." @default.
- W2969055364 created "2019-08-22" @default.
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- W2969055364 date "2007-12-01" @default.
- W2969055364 modified "2023-09-27" @default.
- W2969055364 title "Univoque numbers and a Thue-Morse's avatar" @default.
- W2969055364 hasPublicationYear "2007" @default.
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