no. G4
Algèbre, Théorie des groupes
Sandpile monomorphisms and limits
Lang, Moritz1   ; Shkolnikov, Mikhail2
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
Comptes Rendus. Mathématique, Tome 360 (2022) no. G4, pp. 333-341.

We introduce a tiling problem between bounded open convex polyforms P ^⊂ℝ 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 =ℤ Γ 1 /Δ(ℤ Γ 1 ) on Γ 1 =P ^ 1 ∩ℤ 2 to the one on Γ 2 =P ^ 2 ∩ℤ 2 . We provide several examples of infinite series of such tilings converging to ℝ 2 , and thus define the limit of the sandpile group on the plane.

Reçu le :
Révisé le :
Accepté le :
Publié le :
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, Tome 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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