The Sandpile Group of a Tree

Details The Sandpile Group of a Tree The Sandpile Group of a Tree

2007-03-29

arxiv.org/abs/math/0703868v2

European Journal of Combinatorics 30(4): 1026--1035, 2009

Mathematics

Combinatorics

v2 incorporates referee comments, corrects references, improves notation

Scientific paper

10.1016/j.ejc.2008.02.014

A wired tree is a graph obtained from a tree by collapsing the leaves to a single vertex. We describe a pair of short exact sequences relating the sandpile group of a wired tree to the sandpile groups of its principal subtrees. In the case of a regular tree these sequences split, enabling us to compute the full decomposition of the sandpile group as a product of cyclic groups. This resolves in the affirmative a conjecture of E. Toumpakari concerning the ranks of the Sylow p-subgroups.

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