Economic and social institutions : modelling the evolution paths for the Archaic Society

Evolution of society is considered to be a result of development of social reproduction systems. The leading role in this process is played by the development of the creative and active parts of society where package discoveries and inventions form the basis of the dominant technology of production. Our paper presents a complex economic model of the system with the social reproduction as a set of reproduction kernels and a net of reproduction cycles. We use mapping of permutations to graphs for demonstrating that the evolution of society can be represented as a sequence of nested sub-groups  in group lattices. Evolution paths and their complexity can be evaluated using the graph theory and the complexity criteria. Our findings show that these complexities correspond to those of the spectrum of cycles of the collective economy so that social constants can be calculated and used to describe transition between evolution phases from the Mesolithic to Neolithic age. This allows us to reconstruct a group-lattice of the evolution of society using mathematical methods.