24 citations · 43 across the 12 of their papers we have counts for
8 papers · 1 filter
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…
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…
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.
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…