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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.

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