Sandpiles

Carlos A. Alfaro and Criel Merino ()
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Carlos A. Alfaro: Banco de México
Criel Merino: Universidad Nacional Autónoma de México, Instituto de Matemáticas

A chapter in Handbook of Visual, Experimental and Computational Mathematics, 2026, pp 223-250 from Springer

Abstract: Abstract The most known version of the Abelian sandpile model consists of a set of n sites labeled 1 , 2 , … , n $$1, 2,\ldots , n$$ . At each site, the quantity of grains (or height) of the sandpile is given by an integer h i $$h_i$$ . The vector ( h 1 , … , h n $$h_1,\ldots ,h_n$$ ) is called the configuration of the system. For every site, a threshold H i $$H_i$$ is also defined; a sandpile with h i

Keywords: Graph; Sandpile model; Toppling; Recurrent configuration; Stable configuration; Chip firing game; Spanning tree; Domino tiling; Critical ideal (search for similar items in EconPapers)
Date: 2026
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DOI: 10.1007/978-3-032-16368-4_10

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