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The gonality of chess graphs

2024/03/06 by Nila Cibu, Kexin Ding, Cibu, Nila +11
Computer Science · #05C57 #14T99 #Algebraic Geometry (math.AG) #Artificial Intelligence in Games #Combinatorics (math.CO) #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.2403.03907

openalex publication_date 2024/03/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Chess graphs encode the moves that a particular chess piece can make on an m× n chessboard. We study through these graphs through the lens of chip-firing games and graph gonality. We provide upper and lower bounds for the gonality of king's, bishop's, and knight's graphs, as well as for the toroidal versions of these graphs. We also prove that among all chess graphs, there exists an upper bound on gonality solely in terms of min\m,n\, except for queen's, toroidal queen's, rook's, and toroidal bishop's graphs.

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