Algebra, Group theory
Sandpile monomorphisms and limits
Comptes Rendus. Mathématique, Volume 360 (2022) no. G4, 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
Lang, Moritz 1; Shkolnikov, Mikhail 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
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Lang, Moritz; Shkolnikov, Mikhail. Sandpile monomorphisms and limits. Comptes Rendus. Mathématique, Volume 360 (2022) no. G4, pp. 333-341. doi : 10.5802/crmath.291. http://www.numdam.org/articles/10.5802/crmath.291/

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