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The Lattice Structure of Equally Extended Signed Partitions : A generalization of the Brylawski approach to integer partitions with a p-n junction between two semiconductors model

Cattaneo G., Chiaselotti G., Gentile T., Oliverio P. A.

Fundamenta Informaticae

2015

Vol. 141, nr 1

1--36

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.

Partition Function Formalism in the Problem of Multidimensional Integer Partitions

Rovenchak A.

Computational Methods in Science and Technology

2010

Vol. 16, No. 2

187-190

The formalism based on the microcanonical treatment of a many-boson system is applied to the problem in the number theory known as the partitioning of an integer. An estimation is obtained for the asymptotic behavior of the number of multidimensional partitions into sums of various powers of integers. The obtained results are shown to reproduce the known ones for linear summands.