Polynomial ideals for sandpiles and their Gröbner bases

Authors:
Robert Cori;Dominique Rossin;Bruno Salvy
Affiliations:
Univ. Brodeaux, École polytechnique, France;École polytechnique, France;Algorithms Project, Inria Rocquencourt, France
Venue:
Theoretical Computer Science
Year:
2002

Citing 3
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Chip-firing games, potential theory on graphs, and spanning trees

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Abstract

A polynomial ideal encoding topplings in the abelian sandpile model on a graph is introduced. A Grbner 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.