On Inversion Graphs of Permutations
Sean Mandrick

TL;DR
This paper investigates the structure of inversion graphs derived from permutations, connecting combinatorics, geometry, and poset theory to uncover their complex properties.
Contribution
It provides a comprehensive analysis of inversion graphs of permutations, integrating multiple perspectives to deepen understanding of their combinatorial structure.
Findings
Characterization of inversion graphs in various contexts
Connections between inversion graphs and geometric/poset structures
Insights into the combinatorial properties of permutation inversion graphs
Abstract
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.
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Taxonomy
TopicsAdvanced Combinatorial Mathematics · Advanced Graph Theory Research · Computational Geometry and Mesh Generation
