Union of sets of lengths of numerical semigroups

2019/06/04 by J. I. García-García, García-García, J. I., D. Marín-Aragón +3
Mathematics · #20M05 #20M14 #Advanced Topics in Algebra #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Rings, Modules, and Algebras

paper · pdf · doi:10.48550/arxiv.1906.01266

openalex publication_date 2019/06/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let S=⟨ a₁,…,a_p⟩ be a numerical semigroup, s∈ S and \sf z(s) its set of factorizations. The set of length is denoted by \mathcal L(s)=\\tt L(x₁,…,x_p)| (x₁,…,x_p)∈\sf Z(s)\ where \tt L(x₁,…,x_p)=x₁+…+x_p. From these definitions, the following sets can be defined \textsf W(n)=\s∈ S| ∃ x∈\sf z(s) \textrm such that \ttL(x)=n\, ν(n)=∪_s∈ \textsf W(n) \mathcal L(s)=\l₁

Related

• Factorizations into irreducible numerical semigroups
• The structure theorem for sets of length for numerical semigroups
• Elements with unique length factorization of a numerical semigroup generated by three consecutive numbers
• Length density and numerical semigroups
• Extremal factorization lengths of elements in commutative, cancellative semigroups