On the Gonality of Ferrers Rook Graphs
A Ferrers rook graph is a graph whose vertices correspond to the dots in a Ferrers diagram, and where two vertices are adjacent if they are in the same row or the same column. We propose a conjectural formula for the gonality of Ferrers rook graphs, and prove this conjecture for a few infinite families of Ferrers diagrams. We also prove the conjecture for all Ferrers diagrams $F$ with $|F| \leq 8$.
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