2023/03/22 by M. A. Moreno-Frías, J. C. Rosales, Moreno-Frías, M. A. +1 · 1 citation
Mathematics · Computer Science · #Commutative Algebra and Its Applications #Polynomial and algebraic computation
paper · pdf · doi:10.48550/arxiv.2303.12470
In this work we will show that if F is a positive integer, then the set Arf(F)=\S| S is an Arf numerical semigroup with Frobenius number F\ verifies the following conditions: 1) Δ(F)=\0,F+1,→\ is the minimum of Arf(F), 2) if \S, T\ ⊆ Arf(F), then S ∩ T ∈ Arf(F), 3) if S ∈ Arf(F), S≠ Δ(F) and \mathrm m(S)=min (S \backslash \0\), then S\backslash \\mathrm m(S)\ ∈ Arf(F). The previous results will be used to give an algorithm which calculates the set Arf(F). Also we will see that if X⊆ S\backslash Δ(F) for some S∈ Arf(F), then there is the smallest element of Arf(F) containing X.