Publication: On the cardinality of minimal presentations of numerical semigroups
Program
KU-Authors
KU Authors
Co-Authors
Elmacioglu, Ceyhun
Hilmer, Kieran
O’Neill, Christopher
Park-Kaufmann, Hannah
Publication Date
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Type
Embargo Status
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Abstract
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.
Source
Publisher
Combinatorics Consortium
Subject
Semigroup, Finite frobenius ring, Number
Citation
Has Part
Source
Algebraic Combinatorics
Book Series Title
Edition
DOI
10.5802/alco.354