Presentation Title

Bounds on the Number of Irreducible Semigroups of Fixed Frobenius Number

Start Date

November 2016

End Date

November 2016

Location

HUB 355

Type of Presentation

Oral Talk

Abstract

In 2011, Blanco and Rosales gave an algorithm for constructing a directed tree graph whose vertices are the irreducible numerical semigroups with a fixed Frobenius number. Laird and Martinez in 2013 studied the levels of these trees and conjectured what their height would be. In this paper, we will give an exposition on irreducible numerical semigroups. We also present some data supporting this conjecture of Laird and Martinez, and give a lower and upper bound on the number of irreducible numerical semigroups with fixed Frobenius number.

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Nov 12th, 10:00 AM Nov 12th, 10:15 AM

Bounds on the Number of Irreducible Semigroups of Fixed Frobenius Number

HUB 355

In 2011, Blanco and Rosales gave an algorithm for constructing a directed tree graph whose vertices are the irreducible numerical semigroups with a fixed Frobenius number. Laird and Martinez in 2013 studied the levels of these trees and conjectured what their height would be. In this paper, we will give an exposition on irreducible numerical semigroups. We also present some data supporting this conjecture of Laird and Martinez, and give a lower and upper bound on the number of irreducible numerical semigroups with fixed Frobenius number.