Edvin Heggemann: Graphical Arrangements and Their Generalizations

Supervisor: Krishna Menon Puzhankarai
Abstract: With a basis in graphical arrangements, this master thesis presents a directed weighted multigraph structure which allows for a natural graphical representation of hyperplane arrangements which are similar to, but more general than, the Coxeter arrangement of type B. After an initial introduction to fundamental results of hyperplane arrangements and graphical representations, the directed weighted multigraph structure is used to define two families of arrangements having path-like representations. For both families, we establish bijections between their regions and cartesian products of conventional sets, in turn granting insight into the underlying structure of the arrangements. We also consider certain sub-arrangements obtained by removing boolean hyperplanes.