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Polynomial ideals for sandpiles and their Gröbner bases. (English) Zbl 1002.68105
Summary: A polynomial ideal encoding topplings in the abelian sandpile model on a graph is introduced. A Gröbner basis of this ideal is interpreted combinatorially in terms of well-connected subgraphs. This gives rise to algorithms to determine the identity and the operation in the group of recurrent configurations.

68R10 Graph theory (including graph drawing) in computer science
13B10 Morphisms of commutative rings
Full Text: DOI
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