Second-Level Numerical Semigroups

David Llena () and José Carlos Rosales
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David Llena: Departamento de Matemáticas, Universidad de Almería, E-04120 Almería, Spain
José Carlos Rosales: Departamento de Álgebra, E-18071 Granada, Spain

Mathematics, 2025, vol. 13, issue 4, 1-14

Abstract: Let S be a numerical semigroup with multiplicity m ( S ) . Then, S is called a second-level numerical semigroup if x + y + z − m ( S ) ∈ S for every { x , y , z } ⊆ S ∖ { 0 } . In this paper, we present some algorithms to compute all the second-level numerical semigroups with multiplicity, genus, and a Frobenius fixed number. For m and r , which are positive integers, such that m < r and gcd ( m , r ) = 1 , we show that there exists the minimal second-level numerical semigroup with multiplicity m containing r . We solve the Frobenius problem for these semigroups and show that they satisfy Wilf’s conjecture.

Keywords: numerical semigroups; Frobenius number; genus; embedding dimension; Wilf’s conjecture (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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