4 citations · 10 across the 15 of their papers we have counts for
17 papers
On A Family Of 2-Automatic Sequences Derived From Ultimately Periodic Sequences And Generating Algebraic Continued Fractions In F2((1/T))
Alain Lasjaunias
By replacing the letters to polynomials in F_2[t], an infinite word, over a finite alphabet, can be seen as the sequence of partial quotients of a continued fraction in F_2((1/t)).…
Period-doubling Continued Fractions are Algebraic in Characteristic
Yining Hu, Alain Lasjaunias
Considering an arbitrary pair of distinct and non constant polynomials, and in , we build a continued fraction in whose partial quoti…
A note on hyperquadratic elements of low algebraic degree
Alain Lasjaunias
In different areas of discrete mathematics, a certain type of polynomials, having coefficients in a field K of finite characteristic, has been considered. The form and the degree o…
On particular families of hyperquadratic continued fractions in power series fields of odd characteristic
Alain Lasjaunias
We discuss the form of certain algebraic continued fractions in the field of power series over , where p is an odd prime number. This leads to give explicit continued fraction…
Continued Fractions
Alain Lasjaunias
We present a general introduction to continued fractions, with special consideration to the function fields case. These notes were prepared for a summer class given this year in Be…
On a particular hyperquadratic continued fraction in F(p) with p>2
Alain Lasjaunias
Given an odd prime number p, we describe a continued fraction in the field F(p) of power series in 1/T with coefficients in the finite field F_p, where T is a formal indeterminate.…
A short history of some recent research on continued fractions in function fields
Alain Lasjaunias
The goal of this survey paper is to present, in chronological order, certain research works on continued fractions in power series fields over a finite field, all of them being der…
On a two-valued sequence and related continued fractions in power series fields
Bill Allombert, Nicolas Brisebarre, Alain Lasjaunias
We explicitly describe a noteworthy transcendental continued fraction in the field of power series over Q, having irrationality measure equal to 3. This continued fraction is a gen…
On certain recurrent and automatic sequences in finite fields
Alain Lasjaunias, Jia-Yan Yao
In this work we extend our study on a link between automaticity and certain algebraic power series over finite fields. Our starting point is a family of sequences in a finite field…
A note on hyperquadratic continued fractions in characteristic 2 with partial quotients of degree 1
Alain Lasjaunias
In this note, we describe a family of particular algebraic, and nonquadratic, power series over an arbitrary finite field of characteristic 2, having a continued fraction expansion…
Hyperquadratic continued fractions and automatic sequences
Alain Lasjaunias, Jia-Yan Yao
The aim of this note is to show the existence of a correspondance between certain algebraic continued fractions in fields of power series over a finite field and automatic sequence…
On a quartic equation and two families of hyperquadratic continued fractions in power series fields
Alain Lasjaunias, Khalil Ayadi
Casually introduced thirty years ago, a simple algebraic equation of degree 4, with coefficients in Fp[T], has a solution in the field of power series in 1/T, over the finite field…
Hyperquadratic continued fractions over a finite field of odd characteristic with partial quotients of degree 1
Alain Lasjaunias, Jia-Yan Yao
In 1986, some examples of algebraic, and nonquadratic, power series over a finite prime field, having a continued fraction expansion with partial quotients all of degree one, were…
On hyperquadratic continued fractions in power series fields over a finite field
Alain Lasjaunias
The first part of this note is a short introduction on continued fraction expansions for certain algebraic power series. In the last part, as an illustration, we present a family o…
Quartic Power Series in $\f_3((t^{-1}))$
Alain Lasjaunias, Domingo gomez
We are concerned with power series in 1/T over a finite field of 3 elements $\F_3$. In a previous article, Alain Lasjaunias investigated the existence of particular power series of…
On the continued fraction expansion of the unique root in F(p) of the equation x^4+x^2-Tx-1:12=0 and other related hyperquadratic expansions
Alain Lasjaunias
In 1985, Robbins observed by computer the continued fraction expansion of certain algebraic power series over a finite field. Incidentally, he came across a particular equation of…
Algebraic continued fractions in F_q((T^{-1})) and recurrent sequences in F_q
Alain Lasjaunias
There exists a particular subset of algebraic power series over a finite field which, for different reasons, can be compared to the subset of quadratic real numbers. The continued…