Discrete Geometry & Combinatorics Seminar

Event Date: 

Wednesday, November 16, 2016 - 2:00pm to 3:00pm

Event Location: 

  • South Hall 4607B

Speaker: Sherilyn Tamagawa

Title: The Catenary Degree: A Combinatorial Non-Unique Factorization Invariant

Abstract: We usually like to talk about unique factorization domains, but what happens when an element is not uniquely factorable?

Is there a way to tell how "far" it is from being uniquely factorable? In this talk, we will define the catenary degree, which is one way of measuring non-uniqueness of factorizations. Along the way, we will define a metric on factorizations of an element. We will focus our attention on arithmetical congruence monoids (ACMs), a multiplicative subset of the natural numbers. Our main result will characterize the catenary degree of a special class of ACM. This talk should be accessible to everyone.

This work was joint with Scott Chapman and Theo McKenzie, at the PURE Math REU 2013