Ben Gillen & Jonathan Michala, USC

Abstract: Rothe diagrams are diagrams which track inversions of a permutation. The southwest and numbering properties of these diagrams are known, and we provide some novel properties. We prove which subsets of these properties are necessary to fully characterize a Rothe Diagram. We also prove when a set of ordered, freely floating, non-empty columns can be arranged into a Rothe Diagram. This arrangement is unique and completely determined by the properties we have discovered.