The Lattice Structure of Equally Extended Signed Partitions

Subtitle: A generalization of the Brylawski approach to integer partitions with a p-n junction between two semiconductors model

Article type: Research Article

Authors: Cattaneo, Gianpiero^{a; *} | Chiaselotti, Giampiero^b | Gentile, Tommaso^{b; ‡} | Oliverio, Paolo A.^b

Affiliations: [a] Department of Informatics, Systems and Communications, University of Milano-Bicocca, 20126 Milano, Italy. cattang@live.it; cattang@fislab.disco.unimib.it | [b] Department of Mathematics and Informatics, University of Calabria, 87036 Arcavacata di Rende (CS), Italy. chiaselotti@unical.it; gentile@mat.unical.it; oliverio@unical.it

Note: [*] Address for correspondence: Department of Informatics, Systems and Communications, University ofMilano-Bicocca, 20126 Milano, Italy

Note: [‡] Also works: Istituto Nazionale di Fisica Matematica, Gruppo Collegato di Cosenza, 87036 Arcavacata di Rende (CS), Italy.

Abstract: Signed partitions are used in order to describe a new discrete dynamical model whose configurations have fixed sum and whose evolution rules act in balancing from left and right on the configurations of the system. The resulting model can be considered as an extension to the case of signed partitions of the discrete dynamical system introduced by Brylawski in his classical paper concerning the dominance order of integer partitions. We provide a possible interpretation of our model as a simplified description of p – n junction between two semiconductors. We also show as our model can be embedded in a specific Brylawski dynamical system by means of the introduction of a new evolution rule.

Keywords: Discrete Dynamical Systems, Integer Partitions, Lattices, Evolution Rules

DOI: 10.3233/FI-2015-1261

Journal: Fundamenta Informaticae, vol. 141, no. 1, pp. 1-36, 2015