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- W2951308058 abstract "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." @default.
- W2951308058 created "2019-06-27" @default.
- W2951308058 creator A5007913596 @default.
- W2951308058 date "2004-03-13" @default.
- W2951308058 modified "2023-09-27" @default.
- W2951308058 title "On the sandpile group of regular trees" @default.
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- W2951308058 hasPublicationYear "2004" @default.
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