Elements with unique length factorization of a numerical semigroup generated by three consecutive numbers

2024/04/09 by Pedro A. García-Sánchez, Laura González, García-Sánchez, Pedro A. +3
Engineering · Mathematics · #20M14 #Advanced Theoretical and Applied Studies in Material Sciences and Geometry #Combinatorics (math.CO) #Commutative Algebra (math.AC) #FOS: Mathematics #Graph theory and applications #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.2404.06358

openalex publication_date 2024/04/09 · openalex created_date 2024/04/12 · openalex updated_date 2026/07/28

Abstract

Let S be the numerical semigroup generated by three consecutive numbers a,a+1,a+2, where a∈ℕ, a≥ 3. We describe the elements of S whose factorizations have all the same length, as well as the set of factorizations of each of these elements. We give natural partitions of this subset of S in terms of the length and the denumerant. By using Apéry sets and Betti elements we are able to extend some results, first obtained by elementary means.

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