Abstract
The goal of this thesis is to study the combinatorics of signed exceptional sequences. We will focus on two combinatorial aspects, reflection groups and graph theory. In Chapter 1, we discuss the motivation of studying signed exceptional sequences as well as the two combinatorial aspects. In Chapter 2, we give some preliminary definitions for them. In Chapter 3, we will describe the connection between signed exceptional sequences and reflection groups and give some representation theoretical results of similar ones obtained in reflection groups. In Chapter 4, we will generalize a bijection between exceptional sequences and trees given by Goulden and Yong to type B and type D and give some applications.