Unboundedness of irreducible decompositions of numerical semigroups

2024/05/17 by Tristram Bogart, Bogart, Tristram, S. A. Seyed Fakhari +1
Computer Science · Decision Sciences · Mathematics · #06F05 #11D07 #20M14 #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Number Theory (math.NT) #Polynomial and algebraic computation #Scheduling and Timetabling Solutions

paper · pdf · doi:10.48550/arxiv.2405.11080

openalex publication_date 2024/05/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We present two families of numerical semigroups and show that for each family, the number of required components in an irreducible decomposition cannot be bounded by any given integer. This gives a negative answer to a question raised by Delgado, García-Sánchez and Rosales.

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