A Discrete Dynamical Model of Signed Partitions

A dynamical system is by definition a system whose state changes with time t. We have a discrete dynamical system when t is an integer or a natural number, and the elements of the system can be obtained in the form u t+1 = F(u t ), where F is some global function which describes the evolution rule of the system (see [1]). In a series of very recentworks, the theory of discrete dynamical systems has been applied in several contexts. In [2], the theory of discrete dynamical systems is applied in order to analyze some models of concurrent computing systems. In [3], a dynamical model of parallel computation on bi-infinite time scale with an approach similar to two-sided symbolic dynamics is constructed. In [4], the authors analyze the orbit structure of parallel discrete dynamical systems over directed dependency graphs, with Boolean functions as global functions. In [5], the authors extend the manner of defining the evolution update of discrete dynamical systems on Boolean functions, without limiting the local functions to being dependent restrictions of a global one. Finally, in [6] is given a complete characterization of the orbit structure of parallel discrete dynamical systems with maxterm and minterm Boolean functions as global functions. In [7], the authors have introduced the poset (S(n, d, r), ⊑) of all the signed integer partitions r ≥ a r ≥ ⋅ ⋅ ⋅ ≥