A 2011 paper by Blanco and Rosales describes an algorithm for constructing a directed tree graph of irreducible numerical semigroups of fixed Frobenius numbers. This paper will provide an overview of irreducible numerical semigroups and the directed tree graphs. We will also present new findings and conjectures concerning the structure of these trees.

Author Bio

Taryn Laird is a junior at Northern Arizona University. She is triple majoring and pursuing a B.S. inMathematics, B.S.Ed. in Mathematics and B.A. in Sociology. She plans on continuing her studies at NAUafter graduating in May of 2015 to obtain a M.S. in Mathematics Education, with the eventual goal ofteaching high school mathematics.

Jose Martinez is a senior at Northern Arizona University, pursuing a B.S. in Mathematics, which he expects to complete in May 2013. He plans to attend NAU in the future to obtain a M.S. in Mathematics, with the eventual goal of obtaining a Ph.D. in Mathematics.