2022/11/29 by Ceyhun Elmacioglu, Elmacioglu, Ceyhun, Kieran Hilmer +7
Computer Science · Mathematics · #Algebraic Geometry and Number Theory #Combinatorics (math.CO) #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Polynomial and algebraic computation
paper · pdf · doi:10.48550/arxiv.2211.16283
openalex publication_date 2022/11/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, we consider the following question: "given the multiplicity m and embedding dimension e of a numerical semigroup S, what can be said about the cardinality η of a minimal presentation of S?" We approach this question from a combinatorial (poset-theoretic) perspective, utilizing the recently-introduced notion of a Kunz nilsemigroup. In addition to making significant headway on this question beyond what was previously known, in the form of both explicit constructions and general bounds, we provide a self-contained introduction to Kunz nilsemigroups that avoids the polyhedral geometry necessary for much of their source material.