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A new discrete dynamical system of signed integer partitions. (English) Zbl 1333.05026

Summary: T. Brylawski [Discrete Math. 6, 201–219 (1973; Zbl 0283.06003)] described the covering property for the domination order on non-negative integer partitions by means of two rules. Recently, in C. Bisi et al. [“Dominance order on signed partitions”, Adv. Geom. (to appear)], G. Cattaneo et al. [“Non uniform cellular automata description of signed partition versions of ice and sand pile models”, Lect. Notes Comput. Sci. 8751, 115–124, (2014); “The lattice structure of equally extended signed partitions. A generalization of the Brylawski approach to integer partitions with two possible models: ice piles and semiconductors”, Fundam. Inform. 141, 1–36 (2015)] the two classical Brylawski covering rules have been generalized in order to obtain a new lattice structure in the more general signed integer partition context. Moreover, in Cattaneo et al. [loc. cit.], the covering rules of the above signed partition lattice have been interpreted as evolution rules of a discrete dynamical model of a two-dimensional p-n semiconductor junction in which each positive number represents a distribution of holes (positive charges) located in a suitable strip at the left semiconductor of the junction and each negative number a distribution of electrons (negative charges) in a corresponding strip at the right semiconductor of the junction.
In this paper we introduce and study a new sub-model of the above dynamical model, which is constructed by using a single vertical evolution rule. This evolution rule describes the natural annihilation of a hole-electron pair at the boundary region of the two semiconductors. We prove several mathematical properties of such new discrete dynamical model and we provide a discussion of its physical properties.

MSC:

05A17 Combinatorial aspects of partitions of integers

Citations:

Zbl 0283.06003
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References:

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