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.
"Parallel Rank of Two Sandpile Models of Signed Integer Partitions." J. Appl. Math. 2013 (SI11) 1 - 12, 2013. https://doi.org/10.1155/2013/292143