Numerical monoids, which are co-finite additive submonoids of the natural numbers have long been studied for their non-unique factorization properties. This talk will focus on two of these properties: elasticity and omega-primality. The elasticity of an element is a coarse measure of how different the lengths of its factorizations can be. We study the set of elasticities for a class of numerical monoids and find its formula. Next we study the omega-primality function, which measures how far an element is from being prime. We analyze the omega-primality to provide a closed form for portions of the function.
This talk assumes no background knowledge of monoids so undergraduates are encouraged to attend!!!
An Introduction to Numerical Monoids