36 citations · 128 across the 18 of their papers we have counts for
21 papers
Distances between factorizations in the Chicken McNugget monoid
Scott Chapman, Pedro Garcia-Sanchez, Christopher O'Neill
We use the Chicken McNugget monoid to demonstrate various factorization properties related to relations and chains of factorizations. We study in depth the catenary and tame degree…
Patterns on Numerical Semigroups
Maria Bras-Amorós, Pedro García-Sánchez
We introduce the notion of pattern for numerical semigroups, which allows us to generalize the definition of Arf numerical semigroups. In this way infinitely many other classes of…
Wilf's conjecture in fixed multiplicity
Winfried Bruns, Pedro Garcia-Sanchez, Christopher O'Neill +1
We give an algorithm to determine whether Wilf's conjecture holds for all numerical semigroups with a given multiplicity , and use it to prove Wilf's conjecture holds whenever $…
Critical binomial ideals of Norhtcott type
P. A. García-Sánchez, D. Llena, I. Ojeda
In this paper, we study a family of binomial ideals defining monomial curves in the dimensional affine space determined by hypersurfaces of the form $x_i^{c_i} - x_1^{u_{i1…
Canonical bases of modules over one dimensional k-algebras
A Abbas, A Assi, Pedro A Garcıa-Sánchez
Let K be a field and denote by K[t], the polynomial ring with coefficients in K. Set A = K[f1,. .. , fs], with f1,. .. , fs K[t]. We give a procedure to calculate the monoid…
On the second Feng-Rao distance of Algebraic Geometry codes related to Arf semigroups
J. I. Farrán, P. A. García-Sánchez, B. A. Heredia
We describe the second (generalized) Feng-Rao distance for elements in an Arf numerical semigroup that are greater than or equal to the conductor of the semigroup. This provides a…
Delta sets for symmetric numerical semigroups with embedding dimension three
P. A. García-Sánchez, D. Llena, A. Moscariello
This work extends the results known for the Delta sets of non-symmetric numerical semigroups with embedding dimension three to the symmetric case. Thus, we have a fast algorithm to…
The second Feng-Rao number for codes coming from telescopic semigroups
José I. Farrán, P. A. García-Sánchez, B. A. Heredia +1
In this manuscript we show that the second Feng-Rao number of any telescopic numerical semigroup agrees with the multiplicity of the semigroup. To achieve this result we first stud…
On the number of L-shapes in embedding dimension four
F. Aguiló-Gost, P. A. García-Sánchez, D. Llena
\textit{Minimum distance diagrams}, also known as \textit{\textsf{L}--shapes}, have been used to study some properties related to \textit{weighted Cayley digraphs} of \textit{degre…
The second Feng-Rao number for codes coming from inductive semigroups
J. I. Farrán, P. A. García-Sánchez
The second Feng-Rao number of every inductive numerical semigroup is explicitly computed. This number determines the asymptotical behaviour of the order bound for the second Hammin…
Bases of subalgebras of K[[x]] and K[x]
Abdallah Assi, Pedro A. García-Sánchez, Vincenzo Micale
Let be formal power series (respectively polynomials) in thevariable . We study the semigroup of orders of the formal series inthe algebra $K[[ f1,\ldots, f\…
Cyclotomic numerical semigroups
Emil-Alexandru Ciolan, Pedro A. García-Sánchez, Pieter Moree
Given a numerical semigroup , we let be its semigroup polynomial. We study cyclotomic numerical semigroups; these are numerical semigroups…
On the weight hierarchy of codes coming from semigroups with two generators
M. Delgado, J. I. Farrán, P. A. García-Sánchez +1
The weight hierarchy of one-point algebraic geometry codes can be estimated by means of the generalized order bounds, which are described in terms of a certain Weierstrass semigrou…
Numerical semigroups problem list
Manuel Delgado, Pedro A. Garcia-Sanchez, José C. Rosales
We propose a list of open problems in numerical semigroups.
Huneke-Wiegand Conjecture for Complete Intersection Numerical Semigroup Rings
Pedro A. Garcia-Sanchez, Micah J. Leamer
We give a positive answer to the Huneke-Wiegand Conjecture for monomial ideals over free numerical semigroup rings, and for two generated monomial ideals over complete intersection…
Nonhomogeneous patterns on numerical semigroups
Maria Bras-Amorós, Pedro A. García-Sánchez, Albert Vico-Oton
Patterns on numerical semigroups are multivariate linear polynomials, and they are said to be admissible if there exists a numerical semigroup such that evaluated at any nonincreas…
Factorization invariants in half-factorial affine semigroups
Pedro A. García-Sánchez, Ignacio Ojeda, Alfredo Sánchez-R. -Navarro
Let be the monoid generated by We introduce the homogeneous catenary degree of $\…
Constructing the set of complete intersection numerical semigroups with a given Frobenius number
Abdallah Assi, Pedro A. García-Sánchez
Delorme suggested that the set of all complete intersection numerical semigroups can be computed recursively. We have implemented this algorithm, and particularized it to several s…
On the generalized Feng-Rao numbers of numerical semigroups generated by intervals
M. Delgado, J. I. Farrán, P. A. García-Sánchez +1
We give some general results concerning the computation of the generalized Feng-Rao numbers of numerical semigroups. In the case of a numerical semigroup generated by an interval,…
Uniquely presented finitely generated commutative monoids
Pedro A. Garcia-Sanchez, Ignacio Ojeda
A finitely generated commutative monoid is uniquely presented if it has only a minimal presentation. We give necessary and sufficient conditions for finitely generated, combinatori…
Computing the number of numerical semigroups using generating functions
Victor Blanco, Pedro A. Garcia-Sanchez, Justo Puerto
This paper presents a new methodology to count the number of numerical semigroups of given genus or Frobenius number. We apply generating function tools to the bounded polyhedron t…