No abstract

No abstract

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. * −→d j c j with (d j c j) j ≥ d j. Then toppling vertex j leads to a configuration c i with (c i) i = 0. Using ǫ leads to the following property of recurrent configurations.