David Llena
Current Organizations / Institutes
The organizations/institutes from the scholar's latest article
Research Subjects
David Llena has a total of 23 co-authors. Here are the top co-authors by number of shared publications:
- Pedro Abelardo García-Sánchez
University of Granada
22 shared publications - Francesc Aguilo
CRAAX@UPC, Advanced Network Architectures Lab (CRAAX), UPC BarcelonaTech, 08800 Vilanova i la Geltrú , Spain
4 shared publications - Jose Carlos Rosales
Department of Algebra, Faculty of Sciences, University of Granada, E-18071 Granada, Spain
4 shared publications - Manuel Delgado
Universidade do Porto
4 shared publications - Alessio Moscariello
Università degli Studi di Catania
3 shared publications - Jose I. Farran
Universidad de Valladolid
3 shared publications
Latest Publications
- 6 May 2025
- Published by Springer Nature in Bulletin of the Malaysian Mathematical Sciences Society
- Vol. 48 (4) , 1-35
Ideal Extensions of Free Commutative Monoids
- 6 May 2025
- Published by Springer Nature in Bulletin of the Malaysian Mathematical Sciences Society
- Vol. 48 (4) , 1-35
Ideal Extensions of Free Commutative Monoids
- Open Access
- 11 February 2025
- Published by MDPI AG in Mathematics
- Vol. 13 (4) , 593
Second-Level Numerical Semigroups
Let S be a numerical semigroup with multiplicity . Then, S is called a second-level numerical semigroup if for every . In this paper, we present some algorithms to compute all the second-level numerical semigroups with multiplicity, genus, and a Frobenius fixed number. For m and r, which are positive integers, such that and , we show that there exists the minimal second-level numerical semigroup with multiplicity m containing r. We solve the Frobenius problem for these semigroups and show that they satisfy Wilf’s conjecture.- 11 February 2025
- Published by MDPI AG in Mathematics
- Vol. 13 (4) , 593
Open AccessSecond-Level Numerical Semigroups
Let S be a numerical semigroup with multiplicity . Then, S is called a second-level numerical semigroup if for every . In this paper, we present some algorithms to compute all the second-level numerical semigroups with multiplicity, genus, and a Frobenius fixed number. For m and r, which are positive integers, such that and , we show that there exists the minimal second-level numerical semigroup with multiplicity m containing r. We solve the Frobenius problem for these semigroups and show that they satisfy Wilf’s conjecture. - 23 July 2024
- Published by Springer Nature in Ricerche di Matematica
- Vol. 74 (2) , 731-749
Numerical semigroups with quasi maximal embedding dimension
- 23 July 2024
- Published by Springer Nature in Ricerche di Matematica
- Vol. 74 (2) , 731-749
Numerical semigroups with quasi maximal embedding dimension
- Open Access
Ideal extensions of free commutative monoids
We introduce a new family of monoids, which we call gap absorbing monoids. Every gap absorbing monoid is an ideal extension of a free commutative monoid. For a gap absorbing monoid $S$ we study its set of atoms and Betti elements, which allows us to show that the catenary degree of $S$ is at most four and that the set of lengths of any element in $S$ is an interval. We also give bounds for the $ω$-primality of any ideal extension of a free commutative monoid. For ideal extensions $S$ of $\mathbb{N}^d$, with $d$ a positive integer, we show that $ω(S)$ is finite if and only if $S$ has finitely many gaps.Open AccessIdeal extensions of free commutative monoids
We introduce a new family of monoids, which we call gap absorbing monoids. Every gap absorbing monoid is an ideal extension of a free commutative monoid. For a gap absorbing monoid $S$ we study its set of atoms and Betti elements, which allows us to show that the catenary degree of $S$ is at most four and that the set of lengths of any element in $S$ is an interval. We also give bounds for the $ω$-primality of any ideal extension of a free commutative monoid. For ideal extensions $S$ of $\mathbb{N}^d$, with $d$ a positive integer, we show that $ω(S)$ is finite if and only if $S$ has finitely many gaps. - 3 June 2022
- Published by National Inquiry Services Center (NISC) in Quaestiones Mathematicae
- Vol. 46 (6) , 1195-1219
Factorization in monoids by stratification of atoms and the Elliott problem
In an additive factorial monoid each element can be represented as a linear combination of irreducible elements (atoms) with uniquely determined coefficients running over all natural numbers.In thi...
- 3 June 2022
- Published by National Inquiry Services Center (NISC) in Quaestiones Mathematicae
- Vol. 46 (6) , 1195-1219
Factorization in monoids by stratification of atoms and the Elliott problem
In an additive factorial monoid each element can be represented as a linear combination of irreducible elements (atoms) with uniquely determined coefficients running over all natural numbers.In thi...
- Open Access
Factorization in monoids by stratification of atoms and the Elliott Problem
In an additive factorial monoid each element can be represented as a linear combination of irreducible elements (atoms) with uniquely determined coefficients running over all natural numbers. In this paper we develop for a wide class of non-factorial monoids a concept of stratification for atoms which allows to represent each element as a linear combination of atoms where the coefficients are uniquely determined when restricted in a particular way. This wide class includes inside factorial monoids and in particular simplicial affine semigroups. In the latter case the question of uniqueness is related to a problem studied by E. B. Elliott in a paper from 1903. For the monoid of all nonnegative solutions of a certain linear Diophantine equation in three variables, Elliott considers "simple sets of solutions" (atoms of the monoid) and looks for a method that gives "every set once only". We show that for simplicial affine semigroups in two dimensions a stratification is always possible, which answers to Elliott's problem also for the cases he left open. The results in this paper on the stratification of atoms for monoids in general may be seen also as an answer to a "generalized Elliott problem".
Open AccessFactorization in monoids by stratification of atoms and the Elliott Problem
In an additive factorial monoid each element can be represented as a linear combination of irreducible elements (atoms) with uniquely determined coefficients running over all natural numbers. In this paper we develop for a wide class of non-factorial monoids a concept of stratification for atoms which allows to represent each element as a linear combination of atoms where the coefficients are uniquely determined when restricted in a particular way. This wide class includes inside factorial monoids and in particular simplicial affine semigroups. In the latter case the question of uniqueness is related to a problem studied by E. B. Elliott in a paper from 1903. For the monoid of all nonnegative solutions of a certain linear Diophantine equation in three variables, Elliott considers "simple sets of solutions" (atoms of the monoid) and looks for a method that gives "every set once only". We show that for simplicial affine semigroups in two dimensions a stratification is always possible, which answers to Elliott's problem also for the cases he left open. The results in this paper on the stratification of atoms for monoids in general may be seen also as an answer to a "generalized Elliott problem".
- 16 November 2020
- Published by Cambridge University Press (CUP) in Journal of the Australian Mathematical Society
- Vol. 110 (1) , 48-70
CRITICAL BINOMIAL IDEALS OF NORTHCOTT TYPE
In this paper, we study a family of binomial ideals defining monomial curves in the n-dimensional affine space determined by n hypersurfaces of the form $x_i^{c_i} - x_1^{u_{i1}} \cdots x_n^{u_{1n}}$ in $\Bbbk [x_1, \ldots , x_n]$ with $u_{ii} = 0, \ i\in \{ 1, \ldots , n\}$ . We prove that the monomial curves in that family are set-theoretic complete intersections. Moreover, if the monomial curve is irreducible, we compute some invariants such as genus, type and Frobenius number of the corresponding numerical semigroup. We also describe a method to produce set-theoretic complete intersection semigroup ideals of arbitrary large height.- 16 November 2020
- Published by Cambridge University Press (CUP) in Journal of the Australian Mathematical Society
- Vol. 110 (1) , 48-70
CRITICAL BINOMIAL IDEALS OF NORTHCOTT TYPE
In this paper, we study a family of binomial ideals defining monomial curves in the n-dimensional affine space determined by n hypersurfaces of the form $x_i^{c_i} - x_1^{u_{i1}} \cdots x_n^{u_{1n}}$ in $\Bbbk [x_1, \ldots , x_n]$ with $u_{ii} = 0, \ i\in \{ 1, \ldots , n\}$ . We prove that the monomial curves in that family are set-theoretic complete intersections. Moreover, if the monomial curve is irreducible, we compute some invariants such as genus, type and Frobenius number of the corresponding numerical semigroup. We also describe a method to produce set-theoretic complete intersection semigroup ideals of arbitrary large height.- 1 August 2019
- Published by Elsevier in Journal of Algebra
- Vol. 531, 125-140
Inside factorial monoids and the Cale monoid of a linear Diophantine equation
- 1 August 2019
- Published by Elsevier in Journal of Algebra
- Vol. 531, 125-140
Inside factorial monoids and the Cale monoid of a linear Diophantine equation
- 8 February 2018
- Published by National Inquiry Services Center (NISC) in Quaestiones Mathematicae
- Vol. 41 (8) , 1083-1116
Computing denumerants in numerical 3-semigroups
As far as we know, usual computer algebra packages can not compute denumerants for almost medium (about a hundred digits) or almost medium-large (about a thousand digits) input data in a reasonably time cost on an ordinary computer. Implemented algorithms can manage numerical n-semigroups for small input data.Basically, the denumerant of a non-negative element s ∈ ℕ is the number of non-negative integer solutions of certain linear non-negative Diophantine equation which constant term is equal to s.Here we are interested in denumerants of numerical 3-semigroups which have almost medium input data. A new algorithm for computing denumerants is given for this task. It can manage almost medium input data in the worst case and medium-large or even large input data in some cases.
- 8 February 2018
- Published by National Inquiry Services Center (NISC) in Quaestiones Mathematicae
- Vol. 41 (8) , 1083-1116
Computing denumerants in numerical 3-semigroups
As far as we know, usual computer algebra packages can not compute denumerants for almost medium (about a hundred digits) or almost medium-large (about a thousand digits) input data in a reasonably time cost on an ordinary computer. Implemented algorithms can manage numerical n-semigroups for small input data.Basically, the denumerant of a non-negative element s ∈ ℕ is the number of non-negative integer solutions of certain linear non-negative Diophantine equation which constant term is equal to s.Here we are interested in denumerants of numerical 3-semigroups which have almost medium input data. A new algorithm for computing denumerants is given for this task. It can manage almost medium input data in the worst case and medium-large or even large input data in some cases.
- Open Access
Critical binomial ideals of Norhtcott type
In this paper, we study a family of binomial ideals defining monomial curves in the $n-$dimensional affine space determined by $n$ hypersurfaces of the form $x_i^{c_i} - x_1^{u_{i1}} \cdots x_n^{u_{1n}} \in k[x_1, \ldots, x_n]$ with $u_{ii} = 0$, $i\in \{ 1, \ldots, n\}$. We prove that, the monomial curves in that family are set-theoretic complete intersection. Moreover, if the monomial curve is irreducible, we compute some invariants such as genus, type and Fr\"obenius number of the corresponding numerical semigroup. We also describe a method to produce set-theoretic complete intersection semigroup ideals of arbitrary large height.Open AccessCritical binomial ideals of Norhtcott type
In this paper, we study a family of binomial ideals defining monomial curves in the $n-$dimensional affine space determined by $n$ hypersurfaces of the form $x_i^{c_i} - x_1^{u_{i1}} \cdots x_n^{u_{1n}} \in k[x_1, \ldots, x_n]$ with $u_{ii} = 0$, $i\in \{ 1, \ldots, n\}$. We prove that, the monomial curves in that family are set-theoretic complete intersection. Moreover, if the monomial curve is irreducible, we compute some invariants such as genus, type and Fr\"obenius number of the corresponding numerical semigroup. We also describe a method to produce set-theoretic complete intersection semigroup ideals of arbitrary large height.