We study the self-organized aggregation of a swarm of robots in a closed arena. We assume that the perceptual range of the robots are smaller than the size of the arena and the robots do not have information on the size of the swarm or the arena. Using a probabilistic aggregation behavior model inspired from studies of social insects, we propose a macroscopic model for predicting the final distribution of aggregates in terms of the parameters of the aggregation behavior, the arena size and the sensing characteristics of the robots. Specifically, we use the partition concept, developed in number theory, and its related results to build a discrete-time, non-spatial model of aggregation in swarm robotic systems under a number of simplifying assumptions. We provide simplistic simulations of self-organized aggregation using the aggregation behavior with different parameters and arena sizes. The results show that, despite the fact that the simulations did not explicitly enforce to satisfy the assumptions put forward by the macroscopic model, the final aggregate distributions predicted by the macroscopic model and obtained from simulations match.