Scale-free behavior and universality in random fragmentation and aggregation

Two distinct methods underlying the existence of power-law distribution were studied. The distribution ws stationary under the process of merging and splitting of classes and the distribution of the entities under study was invariant. An explanation for the ubiquitous inverse n relationship in the species abundance relationship in ecology and 1/n2 distribution of company size was also proposed. It was found that the successive splitting and mergers and principle of invariance under recategorization both leads to power law distributions.