Parallel Rank of Two Sandpile Models of Signed Integer Partitions

Abstract

We introduce the concept of fundamental sequence for a finite graded posetXwhich 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 whenXis the finite lattice of all the signed integer partitions such that , where , and whenXis the sublattice of all the signed integer partitions of having exactlydnonzero parts.

Parallel Dynamical Systems over Graphs and Related Topics: A Survey

“…Besides, in [53], a class of lattices and Boolean functions are employed to study the truth of a mathematical conjecture. Other related interesting works in this research line are [54][55][56][57].…”

Rough Sets for n-Cycles and n-Paths

“…Recently, the impetuous development of computer science has placed new questions about the graph structures. For example, the graphs can be studied in terms of sequential dynamical systems (see [2,3,4,5]), by means of parallel dynamics (see [1]), or also for their analogies with both sequential and parallel dynamics on order structures (see [7,8,9,10,15,17,18,19,20,21]). In this paper we continue a research project started in [22,23], where a simple undirected graph is studied as a particular type of information system.…”

On Some Numbers Related to Extremal Combinatorial Sum Problems

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