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pro vyhledávání: '"Ferraguti, Andrea"'
Let $\Sigma=\{a_1, \ldots , a_n\}$ be a set of positive integers with $a_1 < \ldots < a_n$ such that all $2^n$ subset sums are pairwise distinct. A famous conjecture of Erd\H{o}s states that $a_n>C\cdot 2^n$ for some constant $C$, while the best resu
Externí odkaz:
http://arxiv.org/abs/2402.00642
In this paper we give constructions for infinite sequences of finite non-linear locally recoverable codes $\mathcal C\subseteq \prod\limits^N_{i=1}\mathbb F_{q_i}$ over a product of finite fields arising from basis expansions in algebraic number fiel
Externí odkaz:
http://arxiv.org/abs/2304.09071
Autor:
Ferraguti, Andrea, Pagano, Carlo
Andrews and Petsche proposed in 2020 a conjectural characterization of all pairs $(f,\alpha)$, where $f$ is a polynomial over a number field $K$ and $\alpha\in K$, such that the dynamical Galois group of the pair $(f,\alpha)$ is abelian. In this pape
Externí odkaz:
http://arxiv.org/abs/2303.04783
We prove several results on backward orbits of rational functions over number fields. First, we show that if $K$ is a number field, $\phi\in K(x)$ and $\alpha\in K$ then the extension of $K$ generated by the abelian points in the backward orbit of $\
Externí odkaz:
http://arxiv.org/abs/2203.10034
Publikováno v:
In Advances in Mathematics February 2024 438
Good polynomials are the fundamental objects in the Tamo-Barg constructions of Locally Recoverable Codes (LRC). In this paper we classify all good polynomials up to degree $5$, providing explicit bounds on the maximal number $\ell$ of sets of size $r
Externí odkaz:
http://arxiv.org/abs/2104.01434
Autor:
Ferraguti, Andrea, Pagano, Carlo
In this paper, we prove several results on finitely generated dynamical Galois groups attached to quadratic polynomials. First we show that, over global fields, quadratic post-critically finite polynomials are precisely those having an arboreal repre
Externí odkaz:
http://arxiv.org/abs/2004.02847
Autor:
Ferraguti, Andrea, Micheli, Giacomo
Let $q$ be an odd prime power and $n$ be a positive integer. Let $\ell\in \mathbb F_{q^n}[x]$ be a $q$-linearised $t$-scattered polynomial of linearized degree $r$. Let $d=\max\{t,r\}$ be an odd prime number. In this paper we show that under these as
Externí odkaz:
http://arxiv.org/abs/2002.00500
This paper introduces a systematic approach towards the inverse problem for arboreal Galois representations of finite index attached to quadratic polynomials. Let $F$ be a field of characteristic $\neq 2$, $f\in F[x]$ be monic and quadratic and $\rho
Externí odkaz:
http://arxiv.org/abs/1907.08608
Autor:
Ferraguti, Andrea, Micheli, Giacomo
Let $\phi$ be a quadratic, monic polynomial with coefficients in $\mathcal O_{F,D}[t]$, where $\mathcal O_{F,D}$ is a localization of a number ring $\mathcal O_F$. In this paper, we first prove that if $\phi$ is non-square and non-isotrivial, then th
Externí odkaz:
http://arxiv.org/abs/1905.00506