@misc{10481/108765,
year = {2025},
url = {https://hdl.handle.net/10481/108765},
abstract = {Let a and b be positive integers such that a < b and [a, b] = {x ∈ N | a ≤ x ≤
b}. In this work, we will show that A ([a, b]) = {S | S is a numerical semigroup
whose Frobenius number belongs to [a, b]} and is a covariety. This fact allows us to
present an algorithm which computes all the elements from A ([a, b]). We will prove
that A ([a, b], m) = {S ∈ A ([a, b]) | S has multiplicity m} and is a ratio-covariety. As a
consequence, we will show an algorithm which calculates all the elements belonging to
A ([a, b], m). Based on the above results, we will develop an interesting algorithm that
calculates all numerical semigroups with a given multiplicity and complexity.},
organization = {Junta de Andalucía (FQM-298, FQM-343, ProyExcel_00868)},
publisher = {MDPI},
keywords = {Frobenius number},
keywords = {Multiplicity},
keywords = {Algorithm},
title = {The Set of Numerical Semigroups with Frobenius Number Belonging to a Fixed Interval},
doi = {10.3390/math13152538},
author = {Moreno Frías, María Ángeles and Rosales González, José Carlos},
}