#### 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 {*a ^{n}, a^{n }b*, ...,

*ab*,

*b*

^{n}}, the delta set is simply {

*b*−

*a*}. 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(

*b*−

*a*) ≤

*l*− 1, and completely characterize the case where

_{s}*n*= 2 and

*b*−

*a*|

*l*− 1.

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 {*a ^{n}, a^{n }b*, ...,

*ab*,

*b*

^{n}}, the delta set is simply {

*b*−

*a*}. 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(

*b*−

*a*) ≤

*l*− 1, and completely characterize the case where

_{s}*n*= 2 and

*b*−

*a*|

*l*− 1.