%0 Journal Article 
%A Moreno Frías, María Ángeles
%A Rosales, Jose Carlos
%T A Partition of the Set of Numerical Semigroups Associated to Wilf's Conjecture
%D 2025
%@ 1058-6458

%U http://hdl.handle.net/10498/38211
%X If S is a numerical semigroup, we denote by n(S) the cardinality of
N(S) = {s ∈ S | s < F(S)}, F(S) = max(Z\S) and by g(S) the cardinality
of N\S. Let q ∈ Q, q ≥ 1 and {k, F} ⊆ N\{0}. In this paper we
introduce the sets B(q) = {S | S is a numerical semigroupand
g(S)
n(S)
= q}
and A (k, F) = {S ∈ A (k) | F(S) = F}. The Wilf’s conjecture will be
reformulated by these sets. Also we show two algorithms which compute
the elements of the sets A (k, F) = {S ∈ A (k) | F(S) = F} and
B(q, k) = {S | S is a numerical semigroup, g(S) = ak and n(S) = bk}.
%K Numerical semigroup
%K Frobenius number
%K genus
%K embedding dimension
%K Wilf’s conjecture
%~ Universidad de Cádiz