The Sandpile Group of a Tree
Combinatorics
2010-10-08 v2
Abstract
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.
Keywords
Cite
@article{arxiv.math/0703868,
title = {The Sandpile Group of a Tree},
author = {Lionel Levine},
journal= {arXiv preprint arXiv:math/0703868},
year = {2010}
}
Comments
v2 incorporates referee comments, corrects references, improves notation