Arithmetic Varieties of Numerical Semigroups B. Branco, Manuel Ojeda, Ignacio Rosales González, José Carlos Numerical semigroup Varieties Rooted tree In this paper we present the notion of arithmetic variety for numerical semigroups. We study various aspects related to these varieties such as the smallest arithmetic that contains a set of numerical semigroups and we exhibit the rooted tree associated with an arithmetic variety. This tree is not locally finite; however, if the Frobenius number is fixed, the tree has finitely many nodes and algorithms can be developed. All algorithms provided in this article include their (non-debugged) implementation in GAP. 2024-07-23T09:58:03Z 2024-07-23T09:58:03Z 2024-05-22 journal article Branco, M.B., Ojeda, I. & Rosales, J.C. Arithmetic Varieties of Numerical Semigroups. Results Math 79, 171 (2024). [https://doi.org/10.1007/s00025-024-02212-5] https://hdl.handle.net/10481/93398 10.1007/s00025-024-02212-5 eng http://creativecommons.org/licenses/by/4.0/ open access Atribución 4.0 Internacional Springer Nature