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math.CO2012★ 2 cited
A Bijection Between the Recurrent Configurations of a Hereditary Chip-Firing Model and Spanning Trees
Spencer Backman
Hereditary chip-firing models generalize the Abelian sandpile model and the cluster firing model to an exponential family of games induced by covers of the vertex set. This general…
math.CO2012
Infinite Reduction of Divisors on Metric Graphs
Spencer Backman
We demonstrate that the greedy algorithm for reduction of divisors on metric graphs need not terminate by modeling the Euclidean algorithm in this context. We observe that any infi…