No abstract

In combinatorics, a Stirling number of the second kind   , S n k is the number of ways to partition a set of n objects into k nonempty subsets. The empty subsets are also added in the models presented in the article in order to describe properly the absence of the corresponding type i of state in the system, i.e. when its "share". These partitions are well distinguished from the physical point of view, so they are 'typed' differently in the model. Finally, the present developments in the physics of complex systems, in particular the structural relaxation of supercooled liquids and glasses, are discussed by using such stochastic cluster-based models.