Comptes Rendus
Algèbre, Théorie des groupes
Sandpile monomorphisms and limits
Comptes Rendus. Mathématique, Volume 360 (2022), pp. 333-341.

We introduce a tiling problem between bounded open convex polyforms P ^ 2 with colored directed edges. If there exists a tiling of the polyform P ^ 2 by P ^ 1 , we construct a monomorphism from the sandpile group G Γ 1 = Γ 1 /Δ( Γ 1 ) on Γ 1 =P ^ 1 2 to the one on Γ 2 =P ^ 2 2 . We provide several examples of infinite series of such tilings converging to 2 , and thus define the limit of the sandpile group on the plane.

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DOI : 10.5802/crmath.291
Classification : 20K30, 60K35, 47D07

Moritz Lang 1 ; Mikhail Shkolnikov 2

1 University of Applied Sciences Technikum Wien, Höchstädtplatz 6, 1200 Wien, Austria
2 Université de Genève, Section de mathématiques, route de Drize 7, villa Battelle, 1227 Carouge, Switzerland
Licence : CC-BY 4.0
Droits d'auteur : Les auteurs conservent leurs droits
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Moritz Lang; Mikhail Shkolnikov. Sandpile monomorphisms and limits. Comptes Rendus. Mathématique, Volume 360 (2022), pp. 333-341. doi : 10.5802/crmath.291. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.291/

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