C. Marijuán | Universidad de Valladolid (original) (raw)

Papers by C. Marijuán

Research paper thumbnail of Classification of numerical 3-semigroups by means of L-shapes

Semigroup Forum, 2014

We recall L-shapes, which are minimal distance diagrams, related to weighted 2-Cayley digraphs, a... more We recall L-shapes, which are minimal distance diagrams, related to weighted 2-Cayley digraphs, and we give the number and the relation between minimal distance diagrams related to the same digraph. On the other hand, we consider some classes of numerical semigroups useful in the study of curve singularity. Then, we associate L-shapes to each numerical 3-semigroup and we describe some main invariants of numerical 3-semigroups in terms of the associated L-shapes. Finally, we give a characterization of the parameters of the L-shapes associated to a 3-numerical semigroup in terms of its generators, and we use it to classify the numerical 3-semigroups of interest in curve singularity.

Research paper thumbnail of On spectra of weighted graphs of order ≤5

Electronic Notes in Discrete Mathematics

The problem of characterizing the real spectra of weighted graphs is only solved for weighted gra... more The problem of characterizing the real spectra of weighted graphs is only solved for weighted graphs of order n ≤ 4. We overview these known results, that come from the context of nonnegative matrices, and give a new method to rule out many unresolved spectra of size 5.

Research paper thumbnail of Ruling out certain 5-spectra for the symmetric nonnegative inverse eigenvalue problem

Linear Algebra and its Applications

Research paper thumbnail of A map of sufficient conditions for the symmetric nonnegative inverse eigenvalue problem

Linear Algebra and its Applications

The real nonnegative inverse eigenvalue problem (RNIEP) is the problem of determining necessary a... more The real nonnegative inverse eigenvalue problem (RNIEP) is the problem of determining necessary and sufficient conditions for a list of real numbers to be the spectrum of an entrywise nonnegative matrix. A number of sufficient conditions for the existence of such a matrix are known. In this paper, in order to construct a map of sufficient conditions, we compare these conditions and establish inclusion relations or independency relations between them.

Research paper thumbnail of Comparison on the spectral radii of weighted digraphs that differ in a certain subdigraph

Electronic Notes in Discrete Mathematics

Research paper thumbnail of Structural and spectral properties of minimal strong digraphs

Electronic Notes in Discrete Mathematics

In this article, we focus on structural and spectral properties of minimal strong digraphs (MSDs)... more In this article, we focus on structural and spectral properties of minimal strong digraphs (MSDs). We carry out a comparative study of properties of MSDs versus trees. This analysis includes two new properties. The first one gives bounds on the coefficients of characteristic polynomials of trees (double directed trees), and conjectures the generalization of these bounds to MSDs. As a particular case, we prove that the independent coemcient of the characteristic polynomial of a tree or an MSD must be-1, 0 or 1. For trees, this fact means that a tree has at most one perfect matching; for MSDs, it means that an MSD has at most one covering by disjoint cycles. The property states that every MSD can be decomposed in a rooted spanning tree and a forest of reversed rooted trees, as factors. In our opinión, the analogies described suppose a significative change in the traditional point of view about this class of digraphs.

Research paper thumbnail of Symmetric nonnegative realizability via partitioned majorization

Linear and Multilinear Algebra

Research paper thumbnail of Practical challenges that arise when clustering the web using spectral methods

This is a report on an implementation of a spectral clustering algorithm for classifying very lar... more This is a report on an implementation of a spectral clustering algorithm for classifying very large internet sites, with special emphasis on the practical prob-lems encountered in developing such a data mining system. Remarkably some of these technical difficulties are due to fundamental issues pertaining to the mathematics in-volved, and are not treated properly in the literature. Others are inherent to the functions and numerical methods proper to the high level technical computing pro-gramming environment that we use. We will point out what these practical challenges are and how to solve them.

Research paper thumbnail of On Sufficient Conditions for the RNIEP and their Margins of Realizability

Electronic Notes in Discrete Mathematics, 2014

Research paper thumbnail of Submatrix monotonicity of the Perron root, II

Linear Algebra and its Applications, 2014

Research paper thumbnail of Updating a map of sufficient conditions for the real nonnegative inverse eigenvalue problem

Special Matrices

The real nonnegative inverse eigenvalue problem (RNIEP) asks for necessary and sufficient conditi... more The real nonnegative inverse eigenvalue problem (RNIEP) asks for necessary and sufficient conditions in order that a list of real numbers be the spectrum of a nonnegative real matrix. A number of sufficient conditions for the existence of such a matrix are known. The authors gave in [11] a map of sufficient conditions establishing inclusion relations or independency relations between them. Since then new sufficient conditions for the RNIEP have appeared. In this paper we complete and update the map given in [11].

Research paper thumbnail of Higher order relations for a numerical semigroup

Research paper thumbnail of Inequalities for linear combinations of monomials in p-Newton sequences

Research paper thumbnail of The nonnegative inverse eigenvalue problem from the coefficients of the characteristic polynomial. EBL digraphs

The nonnegative inverse eigenvalue problem (NIEP) is: given a family of complex numbers σ={λ1,…,λ... more The nonnegative inverse eigenvalue problem (NIEP) is: given a family of complex numbers σ={λ1,…,λn}, find necessary and sufficient conditions for the existence of a nonnegative matrix A of order n with spectrum σ. Loewy and London [R. Loewy, D. London, A note on the inverse eigenvalue problems for nonnegative matrices, Linear and Multilinear Algebra 6 (1978) 83–90] resolved it for

Research paper thumbnail of Monomial Inequalities for Newton Coefficients and Determinantal Inequalities for p-Newton Matrices

Notions of Positivity and the Geometry of Polynomials, 2011

Research paper thumbnail of Matrices and spectra satisfying the Newton inequalities

Linear Algebra and Its Applications, 2009

An n-by-n real matrix is called a Newton matrix (and its eigenvalues a Newton spectrum) if the no... more An n-by-n real matrix is called a Newton matrix (and its eigenvalues a Newton spectrum) if the normalized coefficients of its characteristic polynomial satisfy the Newton inequalities.A number of basic observations are made about Newton matrices, including closure under inversion, and then it is shown that a Newton matrix with nonnegative coefficients remains Newton under right translations. Those matrices that

Research paper thumbnail of Submatrix monotonicity of the Perron root

Linear Algebra and its Applications, 2012

Research paper thumbnail of A map of sufficient conditions for the real nonnegative inverse eigenvalue problem

Linear Algebra and its Applications, 2007

The real nonnegative inverse eigenvalue problem (RNIEP) is the problem of determining necessary a... more The real nonnegative inverse eigenvalue problem (RNIEP) is the problem of determining necessary and sufficient conditions for a list of real numbers to be the spectrum of an entrywise nonnegative matrix. A number of sufficient conditions for the existence of such a matrix are known. In this paper, in order to construct a map of sufficient conditions, we compare these conditions and establish inclusion relations or independency relations between them.

Research paper thumbnail of Minimal systems of generators for ideals of semigroups

Journal of Pure and Applied Algebra, 1998

We give an algorithmic method to compute a minimal system of generators for I, in the general cas... more We give an algorithmic method to compute a minimal system of generators for I, in the general case of a subsemigroup Sofa finitely generated abelian group, such that Sc~(-S) = {0}.

Research paper thumbnail of Minimal strong digraphs

Discrete Mathematics, 2012

We introduce adequate concepts of expansion of a digraph to obtain a sequential construction of m... more We introduce adequate concepts of expansion of a digraph to obtain a sequential construction of minimal strong digraphs. We characterize the class of minimal strong digraphs whose expansion preserves the property of minimality. We prove that every minimal strong digraph of order n ≥ 2 is the expansion of a minimal strong digraph of order n − 1 and we give sequentially generative procedures for the constructive characterization of the classes of minimal strong digraphs. Finally we describe algorithms to compute unlabeled minimal strong digraphs and their isospectral classes.

Research paper thumbnail of Classification of numerical 3-semigroups by means of L-shapes

Semigroup Forum, 2014

We recall L-shapes, which are minimal distance diagrams, related to weighted 2-Cayley digraphs, a... more We recall L-shapes, which are minimal distance diagrams, related to weighted 2-Cayley digraphs, and we give the number and the relation between minimal distance diagrams related to the same digraph. On the other hand, we consider some classes of numerical semigroups useful in the study of curve singularity. Then, we associate L-shapes to each numerical 3-semigroup and we describe some main invariants of numerical 3-semigroups in terms of the associated L-shapes. Finally, we give a characterization of the parameters of the L-shapes associated to a 3-numerical semigroup in terms of its generators, and we use it to classify the numerical 3-semigroups of interest in curve singularity.

Research paper thumbnail of On spectra of weighted graphs of order ≤5

Electronic Notes in Discrete Mathematics

The problem of characterizing the real spectra of weighted graphs is only solved for weighted gra... more The problem of characterizing the real spectra of weighted graphs is only solved for weighted graphs of order n ≤ 4. We overview these known results, that come from the context of nonnegative matrices, and give a new method to rule out many unresolved spectra of size 5.

Research paper thumbnail of Ruling out certain 5-spectra for the symmetric nonnegative inverse eigenvalue problem

Linear Algebra and its Applications

Research paper thumbnail of A map of sufficient conditions for the symmetric nonnegative inverse eigenvalue problem

Linear Algebra and its Applications

The real nonnegative inverse eigenvalue problem (RNIEP) is the problem of determining necessary a... more The real nonnegative inverse eigenvalue problem (RNIEP) is the problem of determining necessary and sufficient conditions for a list of real numbers to be the spectrum of an entrywise nonnegative matrix. A number of sufficient conditions for the existence of such a matrix are known. In this paper, in order to construct a map of sufficient conditions, we compare these conditions and establish inclusion relations or independency relations between them.

Research paper thumbnail of Comparison on the spectral radii of weighted digraphs that differ in a certain subdigraph

Electronic Notes in Discrete Mathematics

Research paper thumbnail of Structural and spectral properties of minimal strong digraphs

Electronic Notes in Discrete Mathematics

In this article, we focus on structural and spectral properties of minimal strong digraphs (MSDs)... more In this article, we focus on structural and spectral properties of minimal strong digraphs (MSDs). We carry out a comparative study of properties of MSDs versus trees. This analysis includes two new properties. The first one gives bounds on the coefficients of characteristic polynomials of trees (double directed trees), and conjectures the generalization of these bounds to MSDs. As a particular case, we prove that the independent coemcient of the characteristic polynomial of a tree or an MSD must be-1, 0 or 1. For trees, this fact means that a tree has at most one perfect matching; for MSDs, it means that an MSD has at most one covering by disjoint cycles. The property states that every MSD can be decomposed in a rooted spanning tree and a forest of reversed rooted trees, as factors. In our opinión, the analogies described suppose a significative change in the traditional point of view about this class of digraphs.

Research paper thumbnail of Symmetric nonnegative realizability via partitioned majorization

Linear and Multilinear Algebra

Research paper thumbnail of Practical challenges that arise when clustering the web using spectral methods

This is a report on an implementation of a spectral clustering algorithm for classifying very lar... more This is a report on an implementation of a spectral clustering algorithm for classifying very large internet sites, with special emphasis on the practical prob-lems encountered in developing such a data mining system. Remarkably some of these technical difficulties are due to fundamental issues pertaining to the mathematics in-volved, and are not treated properly in the literature. Others are inherent to the functions and numerical methods proper to the high level technical computing pro-gramming environment that we use. We will point out what these practical challenges are and how to solve them.

Research paper thumbnail of On Sufficient Conditions for the RNIEP and their Margins of Realizability

Electronic Notes in Discrete Mathematics, 2014

Research paper thumbnail of Submatrix monotonicity of the Perron root, II

Linear Algebra and its Applications, 2014

Research paper thumbnail of Updating a map of sufficient conditions for the real nonnegative inverse eigenvalue problem

Special Matrices

The real nonnegative inverse eigenvalue problem (RNIEP) asks for necessary and sufficient conditi... more The real nonnegative inverse eigenvalue problem (RNIEP) asks for necessary and sufficient conditions in order that a list of real numbers be the spectrum of a nonnegative real matrix. A number of sufficient conditions for the existence of such a matrix are known. The authors gave in [11] a map of sufficient conditions establishing inclusion relations or independency relations between them. Since then new sufficient conditions for the RNIEP have appeared. In this paper we complete and update the map given in [11].

Research paper thumbnail of Higher order relations for a numerical semigroup

Research paper thumbnail of Inequalities for linear combinations of monomials in p-Newton sequences

Research paper thumbnail of The nonnegative inverse eigenvalue problem from the coefficients of the characteristic polynomial. EBL digraphs

The nonnegative inverse eigenvalue problem (NIEP) is: given a family of complex numbers σ={λ1,…,λ... more The nonnegative inverse eigenvalue problem (NIEP) is: given a family of complex numbers σ={λ1,…,λn}, find necessary and sufficient conditions for the existence of a nonnegative matrix A of order n with spectrum σ. Loewy and London [R. Loewy, D. London, A note on the inverse eigenvalue problems for nonnegative matrices, Linear and Multilinear Algebra 6 (1978) 83–90] resolved it for

Research paper thumbnail of Monomial Inequalities for Newton Coefficients and Determinantal Inequalities for p-Newton Matrices

Notions of Positivity and the Geometry of Polynomials, 2011

Research paper thumbnail of Matrices and spectra satisfying the Newton inequalities

Linear Algebra and Its Applications, 2009

An n-by-n real matrix is called a Newton matrix (and its eigenvalues a Newton spectrum) if the no... more An n-by-n real matrix is called a Newton matrix (and its eigenvalues a Newton spectrum) if the normalized coefficients of its characteristic polynomial satisfy the Newton inequalities.A number of basic observations are made about Newton matrices, including closure under inversion, and then it is shown that a Newton matrix with nonnegative coefficients remains Newton under right translations. Those matrices that

Research paper thumbnail of Submatrix monotonicity of the Perron root

Linear Algebra and its Applications, 2012

Research paper thumbnail of A map of sufficient conditions for the real nonnegative inverse eigenvalue problem

Linear Algebra and its Applications, 2007

The real nonnegative inverse eigenvalue problem (RNIEP) is the problem of determining necessary a... more The real nonnegative inverse eigenvalue problem (RNIEP) is the problem of determining necessary and sufficient conditions for a list of real numbers to be the spectrum of an entrywise nonnegative matrix. A number of sufficient conditions for the existence of such a matrix are known. In this paper, in order to construct a map of sufficient conditions, we compare these conditions and establish inclusion relations or independency relations between them.

Research paper thumbnail of Minimal systems of generators for ideals of semigroups

Journal of Pure and Applied Algebra, 1998

We give an algorithmic method to compute a minimal system of generators for I, in the general cas... more We give an algorithmic method to compute a minimal system of generators for I, in the general case of a subsemigroup Sofa finitely generated abelian group, such that Sc~(-S) = {0}.

Research paper thumbnail of Minimal strong digraphs

Discrete Mathematics, 2012

We introduce adequate concepts of expansion of a digraph to obtain a sequential construction of m... more We introduce adequate concepts of expansion of a digraph to obtain a sequential construction of minimal strong digraphs. We characterize the class of minimal strong digraphs whose expansion preserves the property of minimality. We prove that every minimal strong digraph of order n ≥ 2 is the expansion of a minimal strong digraph of order n − 1 and we give sequentially generative procedures for the constructive characterization of the classes of minimal strong digraphs. Finally we describe algorithms to compute unlabeled minimal strong digraphs and their isospectral classes.