36 citations · 128 across the 18 of their papers we have counts for
7 papers · 1 filter
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…
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 $…
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…
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…
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…
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…