2023/05/23 by M. A. Moreno-Frías, J. C. Rosales, Moreno-Frías, M. A. +1 · 1 citation
Mathematics · Computer Science · #Commutative Algebra and Its Applications #Graph theory and applications #Polynomial and algebraic computation
paper · pdf · doi:10.48550/arxiv.2305.13881
In this work we will show that if F is a positive integer, then Sat(F)=\S| S is a saturated numerical semigroup with Frobenius number F\ is a covariety. As a consequence, we present two algorithms: one that computes Sat(F), and the other which computes all the elements of Sat(F) with a fixed genus. If X⊆ S\backslash Δ(F) for some S∈ Sat(F), then we will see that there is the least element of Sat(F) containing a X. This element will denote by Sat(F)[X]. If S∈Sat(F), then we define the Sat(F)-rank of S as the minimum of \cardinality(X)| S=Sat(F)[X]\. In this paper, also we present an algorithm to compute all the element of Sat(F) with a given Sat(F)-rank.