Parallel Rank of Two Sandpile Models of Signed Integer Partitions. (21st April 2013) - Chiaselotti, G.; Gentile, T.; Marino, G.; Oliverio, P. A.
Abstract : 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 a r, …, a 1, b 1, …, b n − r such that r ≥ a r ≥ ⋯ ≥ a 1 ≥ 0 ≥ b 1 ≥ ⋯ ≥ b n − 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.