β - expansions and ultimately periodic representations par Michel RIGO
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چکیده
β-expansions and ultimately periodic
منابع مشابه
Abstract beta-expansions and ultimately periodic representations
beta-expansions and ultimately periodic representations Michel Rigo, Wolfgang Steiner To cite this version: Michel Rigo, Wolfgang Steiner. Abstract beta-expansions and ultimately periodic representations. Journal de Théorie des Nombres de Bordeaux, Société Arithmétique de Bordeaux, 2005, 17, pp.283-299. HAL Id: hal-00023235 https://hal.archives-ouvertes.fr/hal-00023235 Submitted on 21 Apr 2006 ...
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We compute the cardinality of the syntactic monoid of the language 0∗ repb(mN) made of base b expansions of the multiples of the integer m. We also give lower bounds for the syntactic complexity of any (ultimately) periodic set of integers written in base b. We apply our results to a well studied problem: decide whether or not a b-recognizable set of integers is ultimately periodic.
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We compute the cardinality of the syntactic monoid of the language 0∗ rep b (mN) made of base b expansions of the multiples of the integer m. We also give lower bounds for the syntactic complexity of any (ultimately) periodic set of integers written in base b. We apply our results to some well studied problem: decide whether or not a brecognizable sets of integers is ultimately periodic.
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Consider a non-standard numeration system like the one built over the Fibonacci sequence where nonnegative integers are represented by words over {0, 1} without two consecutive 1. Given a set X of integers such that the language of their greedy representations in this system is accepted by a finite automaton, we consider the problem of deciding whether or not X is a finite union of arithmetic p...
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تاریخ انتشار 2005