RT journal article
T1 Counting the ideals with given genus of a numerical semigroup
A1 Moreno Frías, María Ángeles
A1 Rosales, José Carlos
A2 Matemáticas
K1 Numerical semigroup
K1 ideal
K1 I(S)-semigroup
K1 Frobenius number
K1 genus
K1 multiplicity
K1 genus
K1 ordinary semigroup
AB If S is a numerical semigroup, denote by g(S) the genus of S. A numerical semigroupT is an I(S)-semigroup if T\{0} is an ideal of S. If k ∈ N, then we denote by i(S, k)the number of I(S)-semigroups with genus g(S) + k. In this work, we conjecture thati(S, a) ≤ i(S, b) if a ≤ b, and we show that there is a term from which this sequencebecomes stationary. That is, there exists kS ∈ N such that i(S, kS) = i(S, kS + h)for all h ∈ N. Moreover, we prove that the conjecture is true for ordinary numericalsemigroups, that is, numerical semigroups which the form {0,m,→} for some positiveinteger. Additionally, we calculate the term from which the sequence becomes stationary.
PB World Scientific Publishing Company
SN 0219-4988
YR 2023
FD 2023
LK http://hdl.handle.net/10498/35496
UL http://hdl.handle.net/10498/35496
LA eng
DS Repositorio Institucional de la Universidad de Cádiz
RD 10-may-2026