Journal of Applied Mathematics
Volume 2013 (2013), Article ID 292143, 12 pages
Research Article

Parallel Rank of Two Sandpile Models of Signed Integer Partitions

Dipartimento di Matematica, Universitá della Calabria, Via Pietro Bucci, 87036 Arcavacata di Rende, Italy

Received 4 December 2012; Accepted 24 January 2013

Academic Editor: Filomena Cianciaruso

Copyright © 2013 G. Chiaselotti et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We introduce the concept of fundamental sequence for a finite graded poset X which is also a discrete dynamical model. The concept of fundamental sequence is a refinement of the concept of parallel convergence time for these models. We compute the parallel convergence time and the fundamental sequence when X is the finite lattice of all the signed integer partitions such that , where , and when X is the sublattice of all the signed integer partitions of having exactly d nonzero parts.