Digit systems in polynomial rings over finite fields
TLDR
In this article, the authors define a new kind of digit system in polynomial rings over finite fields, where the ring is a finite field and the digit system is a polynomial in two indeterminates.About:
This article is published in Finite Fields and Their Applications.The article was published on 2003-07-01 and is currently open access. It has received 20 citations till now. The article focuses on the topics: Square-free polynomial & Minimal polynomial (field theory).read more
Citations
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Journal ArticleDOI
Generalized radix representations and dynamical systems I
TL;DR: Families of dynamical systems which are related to generalized radix representations lead to new results on the characterization of bases of Pisot number systems as well as canonical number systems.
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Dynamical directions in numeration
TL;DR: The notion of systeme de numeration fibre unifies the presentation of β-numeration as mentioned in this paper and unifies its application in numeration dynamiques, such as systemes dynamiques which peuvent etre definis dessus.
BookDOI
Combinatorics, Automata and Number Theory
Valrie Berth,Michel Rigo +1 more
TL;DR: In this article, the authors present recent trends arising from the fruitful interaction between the themes of combinatorics on words, automata and formal language theory, and number theory and reveal some of the exciting and important relationships that exist between these different fields.
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Generalized radix representations and dynamical systems II
TL;DR: In this article, a family of dynamical systems which are related to generalized radix representations are studied and the properties of these systems lead to new results on the characterization of bases of Pisot number systems as well as canonical number systems.
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β-Expansions in algebraic function fields over finite fields
TL;DR: The present paper deals with an algebraic function field analogue of @b-expansions of real numbers that completely characterizes the sets with eventually periodic and finite expansions.
References
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Radix representations of quadratic fields
TL;DR: In this paper, an algebraic integer ϱ in a quadratic number field whose minimum polynomial is x 2 + p 1 + p 0 + φ + p 2 + π + p 3 + p 4 + ρ + p p 0 -p p 0 if and only if p 0 ⊾ 2 and −1 ⊽ p 1 ⩽ p 0 −p 1 ⌽p 0.
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Canonical number systems in imaginary quadratic fields
Imre Kátai,Béla Kovács +1 more
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On canonical number systems
TL;DR: A new criterion for the pair {P(x),N} to be a canonical number system is proved, which enables it to be proved that if p2,...,pd1,i=1dpi0 and p0>2i= 1d|pi|, then {P (x,N} is a canonicalNumber system.
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On the characterization of canonical number systems
TL;DR: In this article, the authors introduce the concept of β-expansions, which are representations of real numbers in the unit interval as sums of powers of a real base number β.
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New criteria for canonical number systems
Shigeki Akiyama,Hui Rao +1 more
TL;DR: In this paper, several new criteria for canonical number system generating polynomials are given and a conjecture of S.Akiyama and A.Pethő is proved.