Chip-Firing Games on Banana Trees
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arXiv
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| Auteurs principaux: | , , , , , , , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866909823743819776 |
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| author | Beougher, Marchelle Cibu, Nila Ding, Kexin DiSilvio, Steven Heysse, Kristin Kononova, Sasha Lee, Chan Morrison, Ralph Singal, Krish |
| author_facet | Beougher, Marchelle Cibu, Nila Ding, Kexin DiSilvio, Steven Heysse, Kristin Kononova, Sasha Lee, Chan Morrison, Ralph Singal, Krish |
| contents | We study chip-firing games on multigraphs whose underlying simple graphs are trees, paths, and stars, denoted as banana trees, paths, and stars respectively. We present a polynomial time algorithm to compute the divisorial gonality of banana paths, and give combinatorial formulas for the related invariants of scramble number and screewidth for any banana tree. Furthermore, we leverage banana paths to show that gonality can increase or decrease by an arbitrary amount upon deletion of a single edge, even when the resulting graph is connected. Lastly, we study banana trees and Brill-Noether theory to prove that the gonality conjecture holds for all banana trees. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_03499 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Chip-Firing Games on Banana Trees Beougher, Marchelle Cibu, Nila Ding, Kexin DiSilvio, Steven Heysse, Kristin Kononova, Sasha Lee, Chan Morrison, Ralph Singal, Krish Combinatorics 14T99, 05C57 We study chip-firing games on multigraphs whose underlying simple graphs are trees, paths, and stars, denoted as banana trees, paths, and stars respectively. We present a polynomial time algorithm to compute the divisorial gonality of banana paths, and give combinatorial formulas for the related invariants of scramble number and screewidth for any banana tree. Furthermore, we leverage banana paths to show that gonality can increase or decrease by an arbitrary amount upon deletion of a single edge, even when the resulting graph is connected. Lastly, we study banana trees and Brill-Noether theory to prove that the gonality conjecture holds for all banana trees. |
| title | Chip-Firing Games on Banana Trees |
| topic | Combinatorics 14T99, 05C57 |
| url | https://arxiv.org/abs/2510.03499 |