Arithmetic Varieties of Numerical Semigroups

B. Branco, Manuel; Ojeda, Ignacio; Rosales González, José Carlos

doi:10.1007/s00025-024-02212-5

s00025-024-02212-5.pdf (383.5Kb)

Identificadores

URI: https://hdl.handle.net/10481/93398

DOI: 10.1007/s00025-024-02212-5

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Editorial

Springer Nature

Materia

Numerical semigroup

Varieties

Rooted tree

Fecha

2024-05-22

Referencia bibliográfica

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]

Patrocinador

PID2022-138906NB-C21 funded by MICIU/ AEI/ 10.13039/501100011033; ERDF/EU; Proyecto de Excelencia de la Junta de Andalucía (ProyExcel 00868); Proyecto de investigación del Plan Propio - UCA 2022-2023 (PR2022-011); Research group FQM024 funded by Junta de Extremadura (Spain)/FEDER funds

Resumen

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.

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