On Inversion Graphs of Permutations

In this dissertation, we explore the structure of inversion graphs of permutations–a class of graphs that naturally arises by representing each permutation as a graph, where vertices correspond to entries and edges encode inversions. Advantageously, this class also arises from several other definitions that relate these graphs to geometry and partially ordered sets. By leveraging these different perspectives, we are equipped to gain many insights into their combinatorial intricacies.