RT journal article
T1 The covariety of perfect numerical semigroups with fixed Frobenius number
A1 Moreno Frías, María Ángeles
A1 Rosales, José Carlos
A2 Matemáticas
K1 Perfect numerical semigroup
K1 saturated numerical semigroup
K1 Arf numerical semigroup
K1 covariety
K1 Frobenius number
K1 genus
K1 algorithm
AB Let S be a numerical semigroup. We say that h ∈ N\S is an isolated gap of S if{h−1, h+1} ⊆ S. A numerical semigroup without isolated gaps is called a perfect numericalsemigroup. Denote by m(S) the multiplicity of a numerical semigroup S. A covariety isa nonempty family C of numerical semigroups that fulfills the following conditions: thereexists the minimum of C , the intersection of two elements of C is again an element of C, andS\{m(S)} ∈ C for all S ∈ C such that S 6= min(C ).We prove that the set P(F) = {S : S isa perfect numerical semigroup with Frobenius number F} is a covariety. Also, we describethree algorithms which compute: the set P(F), the maximal elements of P(F), and theelements of P(F) with a given genus. A Parf-semigroup (or Psat-semigroup) is a perfectnumerical semigroup that in addition is an Arf numerical semigroup (or saturated numericalsemigroup), respectively. We prove that the sets Parf(F) = {S : S is a Parf-numericalsemigroup with Frobenius number F} and Psat(F) = {S : S is a Psat-numerical semigroupwith Frobenius number F} are covarieties. As a consequence we present some algorithmsto compute Parf(F) and Psat(F).
PB Institute of Mathematics of the Czech Academy of Sciences
SN 1572-9141
YR 2024
FD 2024
LK http://hdl.handle.net/10498/35406
UL http://hdl.handle.net/10498/35406
LA eng
DS Repositorio Institucional de la Universidad de Cádiz
RD 21-sep-2026