Vol. 14, No. 4, 2021

Download this article
Download this article For screen
For printing
Recent Issues

Volume 14
Issue 4, 541–721
Issue 3, 361–540
Issue 2, 181–360
Issue 1, 1–179

Volume 13, 5 issues

Volume 12, 8 issues

Volume 11, 5 issues

Volume 10, 5 issues

Volume 9, 5 issues

Volume 8, 5 issues

Volume 7, 6 issues

Volume 6, 4 issues

Volume 5, 4 issues

Volume 4, 4 issues

Volume 3, 4 issues

Volume 2, 5 issues

Volume 1, 2 issues

The Journal
About the Journal
Editorial Board
Editors’ Interests
Subscriptions
 
Submission Guidelines
Submission Form
Policies for Authors
Ethics Statement
 
ISSN: 1944-4184 (e-only)
ISSN: 1944-4176 (print)
Author Index
Coming Soon
 
Other MSP Journals
On minimal presentations of shifted affine semigroups with few generators

Christopher O’Neill and Isabel White

Vol. 14 (2021), No. 4, 617–630
Abstract

An affine semigroup is a finitely generated subsemigroup of (0d,+), and a numerical semigroup is an affine semigroup with d = 1. A growing body of recent work examines shifted families of numerical semigroups, that is, families of numerical semigroups of the form Mn = n + r1,,n + rk for fixed r1,,rk, with one semigroup for each value of the shift parameter n. It has been shown that within any shifted family of numerical semigroups, the size of any minimal presentation is bounded (in fact, this size is eventually periodic in n). We consider shifted families of affine semigroups, and demonstrate that some, but not all, shifted families of 4-generated affine semigroups have arbitrarily large minimal presentations.

Keywords
affine semigroup, factorization, shifted semigroup
Mathematical Subject Classification
Primary: 20M14
Milestones
Received: 1 June 2020
Revised: 5 April 2021
Accepted: 6 April 2021
Published: 23 October 2021

Communicated by Scott T. Chapman
Authors
Christopher O’Neill
Department of Mathematics and Statistics
San Diego State University
San Diego, CA
United States
Isabel White
Department of Mathematics and Statistics
San Diego State University
San Diego, CA
United States