F. E. B. Mart'inez

activity

20162025

most citedExtremal product-one free sequences in

C_{q} ⋊_{s} C_{m}

3 citations · 3 across the 12 of their papers we have counts for

collaborators

12 papers

math.GR2025

On minimal product-one sequences of maximal length over the non-abelian group of order $pq$

Danilo Vilela Avelar, Fabio Enrique Brochero Martínez, Sávio Ribas

Let $G$ be a finite group. A sequence over $G$ is a finite multiset of elements of $G$ , and it is called product-one if its terms can be ordered so that their product is the identi…

math.NT2025

The dynamics of a function family over quadratic extensions of finite fields

Fabio E. Brochero Martínez, Hugo R. Teixeira

Let $F_{q}$ be the finite field with $q = p^{s}$ elements, where $p$ is an odd prime and $s$ a positive integer. In this paper, we define the function $f(X)=(cX^q+aX)(X^{q}-X)^{…

math.NT2023

Counting roots of fully triangular polynomials over finite fields

José Gustavo Coelho, Fabio Enrique Brochero Martínez

Let $F_{q}$ be a finite field with $q$ elements, $f \in F_{q} [x_{1}, \dots, x_{n}]$ a polynomial in $n$ variables and let us denote by $N (f)$ the number of roots of $f$ i…

math.NT2023

A note on Bass' conjecture

Danilo Vilela Avelar, Fabio Enrique Brochero Martínez, Sávio Ribas

For a finite group $G$ , we denote by $d (G)$ and by $E (G)$ , respectively, the small Davenport constant and the Gao constant of $G$ . Let $C_{n}$ be the cyclic group of orde…

math.NT2022

On the direct and inverse zero-sum problems over $C_{n} ⋊_{s} C_{2}$

Danilo Vilela Avelar, Fabio Enrique Brochero Martínez, Sávio Ribas

Let $C_{n}$ be the cyclic group of order $n$ . In this paper, we provide the exact values of some zero-sum constants over $C_{n} ⋊_{s} C_{2}$ where $s \neq \equiv \pm 1 (mod n)$ , namely…

cs.DM2022

Dynamics of polynomial maps over finite fields

José Alves Oliveira, Fabio Enrique Brochero Martínez

Let $F_{q}$ be a finite field with $q$ elements and let $n$ be a positive integer. In this paper, we study the digraph associated to the map $x\mapsto x^n h(x^{\frac{q-1}{m}…

math.NT2021

The main zero-sum constants over $D_{2 n} \times C_{2}$

Fabio Enrique Brochero Martínez, Abílio Lemos, B. K. Moriya +1

Let $C_{2}$ be the cyclic group of order $2$ and $D_{2 n}$ be the dihedral group of order $2 n$ , where $n$ is even. In this paper, we provide the exact values of some zero-sum constant…

math.NT2021

Extremal product-one free sequences over $C_{n} ⋊_{s} C_{2}$

Fabio Enrique Brochero Martínez, Sávio Ribas

Let $G$ be a finite group multiplicatively written. The small Davenport constant of $G$ is the maximum positive integer $d (G)$ such that there exists a sequence $S$ of length…

math.NT2020

Artin-Schreier curves given by $F_{q}$ -linearized polynomials

Daniela Oliveira, F. E. Brochero Martínez

Let $F_{q}$ be a finite field with $q$ elements, where $q$ is a power of an odd prime $p$ . In this paper we associate circulant matrices and quadratic forms with the Artin-Sc…

math.NT2019

The estimation of the number of Irreducible Binomials

Fabio Enrique Brochero Martínez, Lays Grazielle Cardoso Silva de Jesus

Let $F_{q}$ be the finite field with $q$ elements, and $T$ a positive integer. In this article we find a sharp estimative of the total number of monic irreducible binomials…

math.NT2018

The ${1, s}$ -weighted Davenport constant in $C_{n}^{k}$

Fabio Enrique Brochero Martínez, Sávio Ribas

Let $G$ be a finite abelian group and let $\emptyset \neq = A \subset Z$ . The $A$ -weighted Davenport constant of $G$ is the smallest positive integer $D_{A} (G)$ such th…

math.NT2016★ 3 cited

Extremal product-one free sequences in $C_{q} ⋊_{s} C_{m}$

Fabio Enrique Brochero Martínez, Sávio Ribas

Let $G$ be a finite group, written multiplicatively. The Davenport constant of $G$ is the smallest positive integer $d$ such that every sequence of $G$ with $d$ elements has a non-…

On minimal product-one sequences of maximal length over the non-abelian group of order pq

The dynamics of a function family over quadratic extensions of finite fields

Counting roots of fully triangular polynomials over finite fields

A note on Bass' conjecture

On the direct and inverse zero-sum problems over Cn​⋊s​C2​

Dynamics of polynomial maps over finite fields

The main zero-sum constants over D2n​×C2​

Extremal product-one free sequences over Cn​⋊s​C2​

Artin-Schreier curves given by Fq​-linearized polynomials

The estimation of the number of Irreducible Binomials

The {1,s}-weighted Davenport constant in Cnk​

Extremal product-one free sequences in Cq​⋊s​Cm​

On minimal product-one sequences of maximal length over the non-abelian group of order $pq$

On the direct and inverse zero-sum problems over $C_{n} ⋊_{s} C_{2}$

The main zero-sum constants over $D_{2 n} \times C_{2}$

Extremal product-one free sequences over $C_{n} ⋊_{s} C_{2}$

Artin-Schreier curves given by $F_{q}$ -linearized polynomials

The ${1, s}$ -weighted Davenport constant in $C_{n}^{k}$

Extremal product-one free sequences in $C_{q} ⋊_{s} C_{m}$