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A note on univoque self-sturmian numbers

Jean-Paul Allouche (2008)

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

We compare two sets of (infinite) binary sequences whose suffixes satisfy extremal conditions: one occurs when studying iterations of unimodal continuous maps from the unit interval into itself, but it also characterizes univoque real numbers; the other is a disguised version of the set of characteristic sturmian sequences. As a corollary to our study we obtain that a real number β in ( 1 , 2 ) is univoque and self-sturmian if and only if the β -expansion of 1 is of the form 1 v , where v is a characteristic...

A note on univoque self-Sturmian numbers

Jean-Paul Allouche (2010)

RAIRO - Theoretical Informatics and Applications

We compare two sets of (infinite) binary sequences whose suffixes satisfy extremal conditions: one occurs when studying iterations of unimodal continuous maps from the unit interval into itself, but it also characterizes univoque real numbers; the other is a disguised version of the set of characteristic Sturmian sequences. As a corollary to our study we obtain that a real number β in (1,2) is univoque and self-Sturmian if and only if the β-expansion of 1 is of the form 1v, where v is a characteristic...

A recursive definition of p -ary addition without carry

François Laubie (1999)

Journal de théorie des nombres de Bordeaux

Let p be a prime number. In this paper we prove that the addition in p -ary without carry admits a recursive definition like in the already known cases p = 2 and p = 3 .

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