Date of Graduation

Spring 2016

Document Type

Honors Research Project

Degree Name

Bachelor of Science

Major

Mathematics - BS/MS

Research Sponsor

Dr. Stefan Forcey

First Reader

Dr. Hung Nguyen

Second Reader

Dr. J.P. Cossey

Abstract

The balanced minimal evolution (BME) polytope arises from the study of phylogenetic trees in biology. It is a geometric structure which has a variant for each natural number n. The main application of this polytope is that we can use linear programming with it in order to determine the most likely phylogenetic tree for a given genetic data set. In this paper, we explore the geometric and combinatorial structure of the BME polytope. Background information will be covered, highlighting some points from previous research, and a new result on the structure of the BME polytope will be given.

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