Geodesic
Determining Genus From Sandpile Torsor Algorithms
Discrete mathematics & theoretical computer science, Tome 23 (2021-2022) no. 1.

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We provide a pair of ribbon graphs that have the same rotor routing and Bernardi sandpile torsors, but different topological genus. This resolves a question posed by M. Chan [Cha]. We also show that if we are given a graph, but not its ribbon structure, along with the rotor routing sandpile torsors, we are able to determine the ribbon graph's genus.
DOI : 10.46298/dmtcs.6176
Classification : 05C10, 05C85 
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McDonough, Alex. Determining Genus From Sandpile Torsor Algorithms. Discrete mathematics & theoretical computer science, Tome 23 (2021-2022) no. 1. doi : 10.46298/dmtcs.6176. http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.6176/

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