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Summary: Univoque numbers and an avatar of
Thue-Morse
Jean-Paul Allouche
CNRS, LRI, UMR 8623
Universit´e Paris-Sud, B^atiment 490
F-91405 Orsay Cedex (France)
allouche@lri.fr
Christiane Frougny
LIAFA, CNRS UMR 7089
Case 7014
75205 Paris Cedex 13 (France)
and Universit´e Paris 8
Christiane.Frougny@liafa.jussieu.fr
Abstract
Univoque numbers are real numbers > 1 such that the num-
ber 1 admits a unique expansion in base , i.e., a unique expansion
1 = j0 aj-(j+1), with aj {0, 1, . . . , - 1} for every j 0.
A variation of this definition was studied in 2002 by Komornik and
Loreti, together with sequences called admissible sequences. We show
how a 1983 study of the first author gives both a result of Ko-
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