Aureliano M. Robles Pérez
Current Organizations / Institutes
The organizations/institutes from the scholar's latest article
Previous Organizations / Institutes
The organizations / institutes from the scholar's other articles in the past ten years
Aureliano M. Robles Pérez has a total of 20 co-authors. Here are the top co-authors by number of shared publications:
- Jose Carlos Rosales
Department of Algebra, Faculty of Sciences, University of Granada, E-18071 Granada, Spain
36 shared publications - Rafael Ortega
Departamento de Matemática Aplicada, Universidad de Granada, Granada, Spain
4 shared publications Jean Mawhin
Institut de Mathématique Pure et Appliquée, Université Catholique de Louvain, 1348-Louvain-la-Neuve, Belgium
3 shared publications- José Martínez-Aroza
FAEG, Facultad de Ciencias, University of Granada, Spain
3 shared publications - Juan Campos
Departamento de Matem_atica Aplicada and Modeling Nature (MNat) Research Unit, Facultad de Ciencias, Universidad de Granada, 18071, Granada, Spain
2 shared publications - Luís Sanchez
Universidade de Lisboa
2 shared publications
Latest Publications
- Open Access
The Frobenius number corresponding to the squares of three consecutive Fibonacci numbers: comparison of three algorithmic processes
We compute the Frobenius number for numerical semigroups generated by the squares of three consecutive Fibonacci numbers. We achieve this by using and comparing three distinct algorithmic approaches: those developed by Ramírez Alfonsín and Rødseth ([15]), Rosales and García-Sánchez ([20]), and Tripathi ([26]).
Open AccessThe Frobenius number corresponding to the squares of three consecutive Fibonacci numbers: comparison of three algorithmic processes
We compute the Frobenius number for numerical semigroups generated by the squares of three consecutive Fibonacci numbers. We achieve this by using and comparing three distinct algorithmic approaches: those developed by Ramírez Alfonsín and Rødseth ([15]), Rosales and García-Sánchez ([20]), and Tripathi ([26]).
- Open Access
- 18 May 2025
- Published by Springer Nature in Arabian Journal of Mathematics
- p. 1-20
The extended Frobenius problem for r-Fibonacci sequences shifted by r-Fibonacci numbers
Using properties of the generalised Zeckendorf decompositions, we study the extended Frobenius problem for sequences of the form $$\{p_a+p_n\}_{n\in {\mathbb {N}}}$$ , where $$\{p_n\}_{n\in {\mathbb {N}}}$$ is an r-Fibonacci sequence and $$p_a$$ is an r-Fibonacci number.- 18 May 2025
- Published by Springer Nature in Arabian Journal of Mathematics
- p. 1-20
Open AccessThe extended Frobenius problem for r-Fibonacci sequences shifted by r-Fibonacci numbers
Using properties of the generalised Zeckendorf decompositions, we study the extended Frobenius problem for sequences of the form $$\{p_a+p_n\}_{n\in {\mathbb {N}}}$$ , where $$\{p_n\}_{n\in {\mathbb {N}}}$$ is an r-Fibonacci sequence and $$p_a$$ is an r-Fibonacci number. - Open Access
- 14 March 2024
- Published by Springer Nature in Bulletin of the Brazilian Mathematical Society, New Series
- Vol. 55 (2) , 1-20
Numerical Semigroups with Monotone Apéry Set and Fixed Multiplicity and Ratio
We characterise the numerical semigroups with a monotone Apéry set (MANS-semigroups for short). Moreover, we describe the families of MANS-semigroups when we fix the multiplicity and the ratio.
- 14 March 2024
- Published by Springer Nature in Bulletin of the Brazilian Mathematical Society, New Series
- Vol. 55 (2) , 1-20
Open AccessNumerical Semigroups with Monotone Apéry Set and Fixed Multiplicity and Ratio
We characterise the numerical semigroups with a monotone Apéry set (MANS-semigroups for short). Moreover, we describe the families of MANS-semigroups when we fix the multiplicity and the ratio.
- Open Access
Numerical semigroups with monotone Apéry set and fixed multiplicity and ratio
We characterise the numerical semigroups with a monotone Ap\'ery set (MANS-semigroups for abbreviate). Moreover, we describe the families of MANS-semigroups when we set the multiplicity and the ratio.
Open AccessNumerical semigroups with monotone Apéry set and fixed multiplicity and ratio
We characterise the numerical semigroups with a monotone Ap\'ery set (MANS-semigroups for abbreviate). Moreover, we describe the families of MANS-semigroups when we set the multiplicity and the ratio.
- Open Access
- 13 October 2023
- Published by Springer Nature in Aequationes mathematicae
- Vol. 98 (2) , 423-440
On sets related to integer partitions with quasi-required elements and disallowed elements
Given a set A of non-negative integers and a set B of positive integers, we are interested in computing all sets C (of positive integers) that are minimal in the family of sets K (of positive integers) such that (i) K contains no elements generated by non-negative integer linear combinations of elements in A and (ii) for any partition of an element in B there is at least one summand that belongs to K. To solve this question, we translate it into a numerical semigroups problem.
- 13 October 2023
- Published by Springer Nature in Aequationes mathematicae
- Vol. 98 (2) , 423-440
Open AccessOn sets related to integer partitions with quasi-required elements and disallowed elements
Given a set A of non-negative integers and a set B of positive integers, we are interested in computing all sets C (of positive integers) that are minimal in the family of sets K (of positive integers) such that (i) K contains no elements generated by non-negative integer linear combinations of elements in A and (ii) for any partition of an element in B there is at least one summand that belongs to K. To solve this question, we translate it into a numerical semigroups problem.
- Open Access
- 24 May 2023
- Published by Springer Nature in Mediterranean Journal of Mathematics
- Vol. 20 (4) , 1-12
The Extended Frobenius Problem for Fibonacci Sequences Incremented by a Fibonacci Number
We study the extended Frobenius problem for sequences of the form $$\{f_a+f_n\}_{n\in \mathbb {N}}$$ , where $$\{f_n\}_{n\in \mathbb {N}}$$ is the Fibonacci sequence and $$f_a$$ is a Fibonacci number. As a consequence of this study, we show that the family of numerical semigroups associated with these sequences satisfies Wilf’s conjecture.- 24 May 2023
- Published by Springer Nature in Mediterranean Journal of Mathematics
- Vol. 20 (4) , 1-12
Open AccessThe Extended Frobenius Problem for Fibonacci Sequences Incremented by a Fibonacci Number
We study the extended Frobenius problem for sequences of the form $$\{f_a+f_n\}_{n\in \mathbb {N}}$$ , where $$\{f_n\}_{n\in \mathbb {N}}$$ is the Fibonacci sequence and $$f_a$$ is a Fibonacci number. As a consequence of this study, we show that the family of numerical semigroups associated with these sequences satisfies Wilf’s conjecture. - Open Access
- 4 March 2023
- Published by Elsevier in Discrete Mathematics
- Vol. 346 (7)
A Frobenius problem suggested by prime k-tuplets
- 4 March 2023
- Published by Elsevier in Discrete Mathematics
- Vol. 346 (7)
Open AccessA Frobenius problem suggested by prime k-tuplets
- Open Access
The extended Frobenius problem for Fibonacci sequences incremented by a Fibonacci number
We study the extended Frobenius problem for sequences of the form $\{f_a+f_n\}_{n\in\mathbb{N}}$, where $\{f_n\}_{n\in\mathbb{N}}$ is the Fibonacci sequence and $f_a$ is a Fibonacci number. As a consequence, we show that the family of numerical semigroups associated to these sequences satisfies the Wilf's conjecture.Open AccessThe extended Frobenius problem for Fibonacci sequences incremented by a Fibonacci number
We study the extended Frobenius problem for sequences of the form $\{f_a+f_n\}_{n\in\mathbb{N}}$, where $\{f_n\}_{n\in\mathbb{N}}$ is the Fibonacci sequence and $f_a$ is a Fibonacci number. As a consequence, we show that the family of numerical semigroups associated to these sequences satisfies the Wilf's conjecture. - Open Access
On sets related to integer partitions with quasi-required elements and disallowed elements
Given a set A of non-negative integers and a set B of positive integers,we are interested in computing all sets C (of positive integers) that are minimal in the family of sets K (of positive integers) such that (i) K contains no elements generated by non-negative integer linear combinations of elements in A and (ii) for any partition of an element in B there is at least one summand that belongs to K. To solve this question, we translate it into a numerical semigroups problem.
Open AccessOn sets related to integer partitions with quasi-required elements and disallowed elements
Given a set A of non-negative integers and a set B of positive integers,we are interested in computing all sets C (of positive integers) that are minimal in the family of sets K (of positive integers) such that (i) K contains no elements generated by non-negative integer linear combinations of elements in A and (ii) for any partition of an element in B there is at least one summand that belongs to K. To solve this question, we translate it into a numerical semigroups problem.
- Open Access
A Frobenius problem suggested by prime $k$-tuplets (extended version)
We study the Frobenius problem for certain k-tuplets, which include prime k-tuplets, in particular prime triplets and prime quadruplets. Moreover, we analyze some properties of the numerical semigroups associated with these tuplets.
Open AccessA Frobenius problem suggested by prime $k$-tuplets (extended version)
We study the Frobenius problem for certain k-tuplets, which include prime k-tuplets, in particular prime triplets and prime quadruplets. Moreover, we analyze some properties of the numerical semigroups associated with these tuplets.