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 heights might be. In this paper, we give an exposition on irreducible numerical semigroups. We also present some data supporting the conjecture of Laird and Martinez, and give a lower and upper bound on the number of irreducible numerical semigroups with fixed Frobenius number.
Bonnand, Clarisse; Booth, Reid; Kaainoa, Carina; and Rooke, Ethan
"Bounds on the Number of Irreducible Semigroups of Fixed Frobenius Number,"
Rose-Hulman Undergraduate Mathematics Journal: Vol. 18:
1, Article 4.
Available at: https://scholar.rose-hulman.edu/rhumj/vol18/iss1/4