Christiane Frougny
University of Paris
76 Papers
323 Citations
Christiane Frougny is an academic researcher from University of Paris. The author has contributed to research in topics: Pisot–Vijayaraghavan number & Integer. The author has an hindex of 19, co-authored 76 publications. Previous affiliations of Christiane Frougny include University of Picardie Jules Verne & Centre national de la recherche scientifique.
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Papers
Finite beta-expansions
TL;DR: In this paper, the authors characterize numbers having finite β-expansions where β belongs to a certain class of Pisot numbers: when the βexpansion of 1 is equal to a1a2am, where a1≥a2≥…≥am≥1 and when the α-expansion for t1t2t2m(tm+1)ω where t1 t2m+1m>t+m+m +1m+tm+n+1
287
Representations of numbers and finite automata
TL;DR: Conditions on the recurrence under which the function of normalization which transforms any representation of an integer into the normal one—obtained by the usual algorithm—can be realized by a finite automaton are given.
147
Palindromic complexity of infinite words associated with simple Parry numbers
TL;DR: In this article, the structure of the Palindromique des mots infinis aperiodiques is described and a description complete of l'ensemble des palindromes, de sa structure and de ses proprietes is given.
Linear numeration systems of order two
TL;DR: A necessary and sufficient condition on the system such that every integer has a canonical representation is given and it is shown that this canonical representation can be computed from any representation by a rational function.
33
Computability by finite automata and Pisot bases
TL;DR: It is proved that the function of normalization in base θ, which maps any θ-representation of a real number onto its ι-development, is a function computable by a finite automaton over any alphabet if and only if θ is a Pisot number.
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