Parallel Rank of Two Sandpile Models of Signed Integer Partitions

Abstract EN

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 P(n,r) of all the signed integer partitions ar,…,a1,b1,…,bn−r such that r≥ar≥⋯≥a1≥0≥b1≥⋯≥bn−r≥−(n−r), where n≥r≥0, and when X is the sublattice P(n,d,r) of all the signed integer partitions of P(n,r) having exactly d nonzero parts.