The gonality of chess graphs
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arXiv
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| Main Authors: | , , , , , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866929266425331712 |
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| author | Cibu, Nila Ding, Kexin DiSilvio, Steven Kononova, Sasha Lee, Chan Morrison, Ralph Singal, Krish |
| author_facet | Cibu, Nila Ding, Kexin DiSilvio, Steven Kononova, Sasha Lee, Chan Morrison, Ralph Singal, Krish |
| contents | Chess graphs encode the moves that a particular chess piece can make on an $m\times n$ 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_03907 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The gonality of chess graphs Cibu, Nila Ding, Kexin DiSilvio, Steven Kononova, Sasha Lee, Chan Morrison, Ralph Singal, Krish Combinatorics Algebraic Geometry 14T99, 05C57 Chess graphs encode the moves that a particular chess piece can make on an $m\times n$ 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. |
| title | The gonality of chess graphs |
| topic | Combinatorics Algebraic Geometry 14T99, 05C57 |
| url | https://arxiv.org/abs/2403.03907 |