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Hereditary chip-firing models generalize the Abelian sandpile model and thecluster firing model to an exponential family of games induced by covers of thevertex set. This generalization retains some desirable properties, e.g.stabilization is independent of firings chosen and each chip-firing equivalenceclass contains a unique recurrent configuration. In this paper we present anexplicit bijection between the recurrent configurations of a hereditarychip-firing model on a graph and its spanning trees.

A Bijection Between the Recurrent Configurations of a Hereditary Chip-Firing Model and Spanning Trees