A Discrete Dynamical Model of Signed Partitions

Abstract

We use a discrete dynamical model with three evolution rules in order to analyze the structure of a partially ordered set of signed integer partitions whose main properties are actually not known. This model is related to the study of some extremal combinatorial sum problems.

Predecessors Existence Problems and Gardens of Eden in Sequential Dynamical Systems

“…Network models are the natural way to formalize the evolution of any phenomenon that includes cells, gens, entities, or any kind of distinct elements which interact among them. Thus, it is not amazing the big amount of papers, published in the last decades, associated with sciences (see, for instance, [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18]) and engineering (see, for instance, [19][20][21][22][23][24]), where such models appear to represent different phenomena and study their behavior.…”

On the Periods of Parallel Dynamical Systems

“…Other tools for mathematical modeling as cellular automata (CA) [5][6][7][8][9][10][11] or Boolean networks (BN) [12][13][14] are particular cases of PDS [15]. It shows the enormous versatility of this new paradigm, which has applications to different branches of sciences as biology [12,16,17], ecology [18][19][20], mathematics [21,22], cryptography [23,24], physics [25], and chemistry [26]. (The abbreviations GDS, PDS, SDS, CA, and BN will be written for the singular and plural forms of the corresponding terms, since it seems better from an aesthetic point of view.…”

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.…”