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On the structure of (−)-integers

Wolfgang Steiner — 2012

RAIRO - Theoretical Informatics and Applications

The (−)-integers are natural generalisations of the -integers, and thus of the integers, for negative real bases. When is the analogue of a Parry number, we describe the structure of the set of (−)-integers by a fixed point of an anti-morphism.

On the structure of (−β)-integers

Wolfgang Steiner — 2012

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

The (−)-integers are natural generalisations of the -integers, and thus of the integers, for negative real bases. When is the analogue of a Parry number, we describe the structure of the set of (−)-integers by a fixed point of an anti-morphism.

The Zeckendorf expansion of polynomial sequences

Michael DrmotaWolfgang Steiner — 2002

Journal de théorie des nombres de Bordeaux

In the first part of the paper we prove that the Zeckendorf sum-of-digits function s z ( n ) and similarly defined functions evaluated on polynomial sequences of positive integers or primes satisfy a central limit theorem. We also prove that the Zeckendorf expansion and the q -ary expansions of integers are asymptotically independent.

Abstract β -expansions and ultimately periodic representations

Michel RigoWolfgang Steiner — 2005

Journal de Théorie des Nombres de Bordeaux

For abstract numeration systems built on exponential regular languages (including those coming from substitutions), we show that the set of real numbers having an ultimately periodic representation is ( β ) if the dominating eigenvalue β > 1 of the automaton accepting the language is a Pisot number. Moreover, if β is neither a Pisot nor a Salem number, then there exist points in ( β ) which do not have any ultimately periodic representation.

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