Longest and shortest factorizations in embedding dimension three

Liu, Baian; Yap, JiaYan

doi:10.2140/involve.2023.16.673

Download this article
	For screen
	For printing

Recent Issues

The Journal

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

This article is available for purchase or by subscription. See below.

Longest and shortest factorizations in embedding dimension three

Baian Liu and JiaYan Yap

Vol. 16 (2023), No. 4, 673–688

DOI: 10.2140/involve.2023.16.673

Abstract

For a numerical monoid $⟨ n_{1}, \dots, n_{k} ⟩$ minimally generated by $n_{1}, \dots, n_{k} \in ℕ$ , with $n_{1} < \dots < n_{k}$ , the longest and shortest factorization lengths of an element $x$ , denoted as $L (x)$ and $ℓ (x)$ , respectively, follow the identities $L (x + n_{1}) = L (x) + 1$ and $ℓ (x + n_{k}) = ℓ (x) + 1$ for sufficiently large elements $x$ . We characterize when these identities hold for all elements of numerical monoids of embedding dimension three.

PDF Access Denied

We have not been able to recognize your IP address 3.144.107.191 as that of a subscriber to this journal.
Online access to the content of recent issues is by subscription, or purchase of single articles.

Please contact your institution's librarian suggesting a subscription, for example by using our journal-recommendation form. Or, visit our subscription page for instructions on purchasing a subscription.

You may also contact us at contact@msp.org
or by using our contact form.

Or, you may purchase this single article for USD 30.00:

Keywords

numerical monoid, factorization length, Betti element

Mathematical Subject Classification

Primary: 11D75, 20M13, 20M14

Milestones

Received: 15 June 2022

Revised: 24 September 2022

Accepted: 10 October 2022

Published: 31 October 2023

Communicated by Scott T. Chapman

Authors

Baian Liu
Department of Mathematics The Ohio State University Columbus, OH United States

JiaYan Yap
Department of Mathematics The Ohio State University Columbus, OH United States

Vol. 16, No. 4, 2023