RT journal article
T1 Digital numerical semigroups
A1 Moreno Frías, María Ángeles
A1 Rosales, José Carlos
K1 Digital numerical semigroup
K1 Frobenius number
K1 genus
K1 multiplicity
K1 algorithm
K1 covariety
K1 Frobenius variety
K1 Frobenius pseudo-variety
AB The number of digits in base ten system of a positive integer n, is denoted by l(n). A digitalsemigroup is a subsemigroup D of (N\{0}, ·) such that if d ∈ D, then {x ∈ N\{0} | l(x) = l(d)} ⊆ D.Let A ⊆ N\{0}. Denote by L(A) = {l(a) | a ∈ A}. We will say that a numerical semigroup S is a digitalnumerical semigroup if there is a digital semigroup D such that S = L(D) ∪ {0}. In this work we show thatD = {S | S is a digital numerical semigroup} is a Frobenius variety, D(Frob=F) = {S ∈ D | F(S) = F} is acovariety and D(mult = m) = {S ∈ D | m(S) = m} is a Frobenius pseudo-variety. As a consequence wepresent some algorithms to compute D(Frob=F), D(mult = m) and D(gen = 1) = {S ∈ D | g(S) = 1}.If X ⊆ N\{0}, we denote by D[X] the smallest element of D containing X. If S = D[X], then we willsay that X is a D-system of generators of S. We will prove that if S ∈ D, then S admits a unique minimalD-system of generators, denoted by Dmsg(S). The cardinality of Dmsg(S) is called the D-rank of S. Wesolve the Frobenius problem to elements of D with D-rank equal to 1. Moreover, we present an algorithmicprocedure to calculate all the elements of D with fixed D-rank.
PB Faculty of Sciences and Mathematics, University of Niˇs, Serbia
YR 2024
FD 2024
LK http://hdl.handle.net/10498/35431
UL http://hdl.handle.net/10498/35431
LA eng
DS Repositorio Institucional de la Universidad de Cádiz
RD 10-may-2026