2014/06/02 by J. I. García-García, M. A. Moreno-Frías, García-García, J. I. +3 · 1 citation
Computer Science · Mathematics · #20M05 (Secondary) #20M14 (Primary) #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Polynomial and algebraic computation #Rings, Modules, and Algebras #math.AC #msc:20M05 #msc:20M14
paper · pdf · doi:10.48550/arxiv.1406.0280
openalex publication_date 2014/06/02 · arxiv created 2014/08/29 · arxiv updated 2014/09/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let \a1,…,ap\ be the minimal generating set of a numerical monoid S. For any s∈ S, its Delta set is defined by Δ(s)=\li-li-1|i=2,…,k\ where \l1<…<lk\ is the set \∑i=1pxi | s=∑i=1pxiai \textrm and xi∈ \N \textrm for all i\. The Delta set of S, denoted by Δ(S), is the union of all the sets Δ(s) with s∈ S. As proved in [S.T. Chapman, R. Hoyer, and N. Kaplan. Delta sets of numerical monoids are eventually periodic. Aequationes Math. 77 (2009), no. 3, 273--279], there exists a bound N such that Δ(S) is the union of the sets Δ(s) with s∈ S and s<N. In this work, by using geometrical tools, we obtain a sharpened bound and we give an algorithm to compute Δ(S) from the factorizations of only a1 elements.