Abstract:We introduce a tiling problem between bounded open convex polyforms P ⊂ R 2 with directed and uniquely colored edges. If there exists a tiling of the polyform P2 by P1, we show that one can construct a monomorphism from the sandpile group GΓ 1 = Z Γ 1 /∆(Z Γ 1 ) on the domain (graph) Γ1 = P1 ∩ Z 2 to the respective group on Γ2 = P2 ∩ Z 2 . We provide several examples of infinite series of such tilings with polyforms converging to R 2 , and thus the first definition of scaling-limits for the sandpile group on t… Show more
Set email alert for when this publication receives citations?
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.