Displaying similar documents to “On multiplicatively dependent linear numeration systems, and periodic points”

Abstract β -expansions and ultimately periodic representations

Michel Rigo, Wolfgang Steiner (2005)

Journal de Théorie des Nombres de Bordeaux

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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.

Binary operations on automatic functions

Juhani Karhumäki, Jarkko Kari, Joachim Kupke (2008)

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

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Real functions on the domain [ 0 , 1 ) n – often used to describe digital images – allow for different well-known types of binary operations. In this note, we recapitulate how weighted finite automata can be used in order to represent those functions and how certain binary operations are reflected in the theory of these automata. Different types of products of automata are employed, including the seldomly-used full cartesian product. We show, however, the infeasibility of functional composition;...

An exercise on Fibonacci representations

Jean Berstel (2001)

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

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We give a partial answer to a question of Carlitz asking for a closed formula for the number of distinct representations of an integer in the Fibonacci base.