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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.

MSC:
68R10Graph theory in connection with computer science (including graph drawing)
13B10Automorphisms, etc. (commutative rings)
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References:
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