1207.6175 (Spencer Backman)

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

Spencer Backman

Hereditary chip-firing models generalize the Abelian sandpile model and the cluster firing model to an exponential family of games. This generalization retains some very desirable properties, e.g. stabilization is independent of firings chosen and each chip-firing equivalence class contains a unique recurrent state. It follows from the second observation that the number of recurrent states in a hereditary chip-firing model is the same as the number of spanning trees. In this paper we present an explicit bijection between the recurrent configurations of a hereditary chip-firing model on a graph and its spanning trees.

View original: http://arxiv.org/abs/1207.6175