24 citations · 43 across the 12 of their papers we have counts for
15 papers
Cyclotomic exponent sequences of numerical semigroups
Alexandru Ciolan, Pedro A. García-Sánchez, Andrés Herrera-Poyatos +1
We study the cyclotomic exponent sequence of a numerical semigroup and we compute its values at the gaps of the elements of with unique representations in terms of mi…
Factorization in monoids by stratification of atoms and the Elliott Problem
Pedro A. García-Sánchez, Ulrich Krause, David Llena
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 natur…
Algorithms for Generalized Numerical Semigroups
Carmelo Cisto, Manuel Delgado, Pedro A. García-Sánchez
We provide algorithms for performing computations in generalized numerical semigroups, that is, submonoids of with finite complement in . These sem…
The monoid of monotone functions on a poset and quasi-arithmetic multiplicities for uniform matroids
Winfried Bruns, Pedro A. García-Sánchez, Luca Moci
We describe the structure of the monoid of natural-valued monotone functions on an arbitrary poset. For this monoid we provide a presentation, a characterization of prime elements,…
Inside factorial monoids and the cale monoid of a single Diophantine equation
Pedro A. García-Sánchez, Ulrich Krause, David Llena
We give a structure theorem for inside factorial domains. As an example we study the monoid of nonnegative integer solutions of equations of the form $a_1x_1+\cdots +a_{r-1}x_{r-1}…
Isolated factorizations and their applications in simplicial affine semigroups
Pedro A. García-Sánchez, Andrés Herrera-Poyatos
We introduce the concept of isolated factorizations of an element of a commutative monoid and study its properties. We give several bounds for the number of isolated factorizations…
The tree of numerical semigroups with low multiplicity
P. A. García-Sánchez, D. Marín-Aragón, A. M. Robles-Pérez
We show that the number of numerical semigroups with multiplicity three, four or five and fixed genus is increasing as a function in the genus. To this end we use the Kunz polytope…
Good subsemigroups of
Marco D'Anna, Pedro A. García-Sánchez, Vincenzo Micale +1
Value semigroups of non irreducible singular algebraic curves and their fractional ideals are submonoids of that are closed under infimums, have a conductor and fulfi…
Delta sets for numerical semigroups with embedding dimension three
Pedro A. García-Sánchez, David Llena, Alessio Moscariello
We present a fast algorithm to compute the Delta set of a nonsymmetric numerical semigroups with embedding dimension three.
On the computation of factorization invariants for affine semigroups
Pedro A. García-Sánchez, Christopher O'Neill, Gautam Webb
We present several new algorithms for computing factorization invariant values over affine semigroups. In particular, we give (i) the first known algorithm to compute the delta set…
Numerical semigroups and applications
Abdallah Assi, Pedro A. García-Sánchez
The aim of this manuscript is to give some basic notions related to numerical semigroups, and from these on the one hand describe a classical application to the study of singularit…
On curves with one place at infinity
Abdallah Assi, Pedro A. García-Sánchez
Let be a plane curve. We give a procedure based on Abhyankar's approximate roots to detect if it has a single place at infinity, and if so construct its associated -sequence…
Frobenius vectors, Hilbert series and gluings
Abdallah Assi, Pedro A. García-Sánchez, Ignacio Ojeda
Let and be two affine semigroups and let be the gluing of and . Several invariants of are then related to those of and ; we review some of…
Affine semigroups having a unique Betti element
Pedro A. García-Sánchez, Ignacio Ojeda, José Carlos Rosales
We characterize affine semigroups having one Betti element and we compute some relevant non-unique factorization invariants for these semigroups. As an example, we particularize ou…
Semigroup-theoretical characterizations of arithmetical invariants with applications to numerical monoids and Krull monoids
Víctor Blanco, Pedro A. García-Sánchez, Alfred Geroldinger
Arithmetical invariants---such as sets of lengths, catenary and tame degrees---describe the non-uniqueness of factorizations in atomic monoids. We study these arithmetical invarian…