On the sandpile group of regular trees
| dc.creator | Toumpakari, Evelin | |
| dc.date | 2004-03-13 | |
| dc.date.accessioned | 2026-07-07T05:06:22Z | |
| dc.date.available | 2026-07-07T05:06:22Z | |
| dc.description | The sandpile group of a connected graph is the group of recurrent configurations in the abelian sandpile model on this graph. We study the structure of this group for the case of regular trees. A description of this group is the following: Let T(d,h) be the d-regular tree of depth h and let V be the set of its vertices. Denote the adjacency matrix of T(d,h) by A and consider the modified Laplacian matrix D:=dI-A. Let the rows of D span the lattice L in Z^V. The sandpile group of T(d,h) is Z^V/L. We compute the rank, the exponent and the order of this abelian group and find a cyclic Hall-subgroup of order (d-1)^h. We find that the base (d-1)-logarithm of the exponent and of the order are asymptotically 3h^2/pi^2 and c_d(d-1)^h, respectively. We conjecture an explicit formula for the ranks of all Sylow subgroups. | |
| dc.description | 24 pages | |
| dc.identifier | https://arxiv.org/abs/math/0403219 | |
| dc.identifier | http://arxiv.org/abs/math/0403219 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/70444 | |
| dc.subject | Combinatorics | |
| dc.subject | 05C50 (Primary) 05C25, 20K01, 82B20 (Secondary) | |
| dc.title | On the sandpile group of regular trees | |
| dc.type | text |