In this paper, we employ the theory of abaci to introduce a model to provide a new combinatorial interpretation for n-connected objects such as polyominoes, polyiamonds, polyhexes, polykites and site animals. The proposed model is called the nested chain abacus model, which involves the construction of an abacus with n beads to represent the n-connected objects and the formulation of the corresponding partition of the abacus. We used the notation of abacus in order to give recognize or describe families of n-connected objects defined by inscribing the n-connected objects in abacus.

n-connected objects, abacus, nested chain abacus, connected partition.