2014/04/09 by Lance Bryant, Bryant, Lance, James Hamblin +1
Computer Science · Mathematics · #13 #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Graph theory and applications #Polynomial and algebraic computation #math.AC #msc:13
paper · pdf · doi:10.48550/arxiv.1404.2629
10 pages, changed some terminology, removed last two sections to streamline article
openalex publication_date 2014/04/09 · arxiv created 2014/07/14 · arxiv updated 2014/07/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We provide a new way to represent numerical semigroups by showing that the position of every Apéry set of a numerical semigroup S in the enumeration of the elements of S is unique, and that S can be re-constructed from this "position vector." We extend the discussion to more general objects called numerical sets, and show that there is a one-to-one correspondence between m-tuples of positive integers and the position vectors of numerical sets closed under addition by m+1. We consider the problem of determining which position vectors correspond to numerical semigroups.