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.

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.