Presentation Title

Delta Sets of Geometric Nonminimally Generated Numerical Monoids

Faculty Mentor

Jay Daigle

Start Date

23-11-2019 8:45 AM

End Date

23-11-2019 9:00 AM

Location

Markstein 303

Session

oral 1

Type of Presentation

Oral Talk

Subject Area

physical_mathematical_sciences

Abstract

A numerical monoid is a subset of the whole numbers with addition as a binary operation, and we can factor elements of a numerical monoid into its generating elements, which form a generating set. When a nonminimal element is included in the generating set, the structure of factorizations and factorization invariants, in particular the delta set, changes. In minimal geometric generating sets of the form {an, an b, ..., ab, bn}, the delta set is simply {ba}. We study the case when a nonminimal element, labeled s, is added to the generating set. In this specialized instance, we prove several basic properties of the delta set, characterize a majority of the case where n = 2 and 2(ba) ≤ ls − 1, and completely characterize the case where n = 2 and ba | l − 1.

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Nov 23rd, 8:45 AM Nov 23rd, 9:00 AM

Delta Sets of Geometric Nonminimally Generated Numerical Monoids

Markstein 303

A numerical monoid is a subset of the whole numbers with addition as a binary operation, and we can factor elements of a numerical monoid into its generating elements, which form a generating set. When a nonminimal element is included in the generating set, the structure of factorizations and factorization invariants, in particular the delta set, changes. In minimal geometric generating sets of the form {an, an b, ..., ab, bn}, the delta set is simply {ba}. We study the case when a nonminimal element, labeled s, is added to the generating set. In this specialized instance, we prove several basic properties of the delta set, characterize a majority of the case where n = 2 and 2(ba) ≤ ls − 1, and completely characterize the case where n = 2 and ba | l − 1.