arXiv subjects

Sean Mandrick

Publications and source records attributed to Sean Mandrick.

3 recordsLinked to original sources

arXiv2026

Chains and unique transitive orientations of prime graphs

We give a short, conceptual proof that prime graphs have at most two transitive orientations, a much-quoted result of Gallai. Our proof uses chains, introduced by Chudnovsky, Kim, Oum, and Seymour, which provide a transparent characterization of primality. Transitivity induces a forcing relation on edges; using chains, we show that any two edges of a prime graph are equivalent under this relation, and thus any transitive orientation is unique up to reversal.

math.CO↗

arXiv2025

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.

math.CO↗

arXiv2023

Bounds on the lettericity of graphs

Lettericity measures the minimum size of an alphabet needed to represent a graph as a letter graph, where vertices are encoded by letters, and edges are determined by an underlying decoder. We prove that all graphs on~$n$ vertices have lettericity at most approximately $n - \tfrac{1}{2} \log_2 n$ and that almost all graphs on $n$ vertices have lettericity at least $n - (2 \log_2 n + 2 \log_2 \log_2 n)$.

math.CO↗