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arXiv · 2405.07947

On the Gonality of Ferrers Rook Graphs

David Jensen·Marissa Morvai·William Welch·Sydney Yeomans
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Abstract

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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David Jensen, Marissa Morvai, William Welch, Sydney Yeomans. 2024-05-13. On the Gonality of Ferrers Rook Graphs. https://arxiv.org/abs/2405.07947

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