The Sandpile Group of a Tree

@misc{citeulike:3042363, 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.}, author = {Levine, Lionel }, citeulike-article-id = {3042363}, eprint = {math/0703868}, keywords = {sandpile, tree}, month = {Jul}, posted-at = {2008-07-25 10:56:13}, priority = {2}, title = {The Sandpile Group of a Tree}, url = {http://arxiv.org/abs/math/0703868}, year = {2008} }

TY - ELEC ID - citeulike:3042363 L3 - citeulike-article-id:3042363 TI - The Sandpile Group of a Tree N2 - 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. KW - sandpile KW - tree AU - Levine, Lionel PY - 2008/Jul/24/ UR - http://arxiv.org/abs/math/0703868 ER -