Partitions and branching processes

A partition, i.e. a division of a finite set into nonempty subsets, is a simple and essential concept of quantitatively understanding the reality. A partition of a number n is a decreasing sequence of natural numbers whose sum equals n. Greater numbers are seen only in terms of the union of partitions. The most important processes such as stochastic processes of branching processes can be expressed most simply using the language of partitions. By means of partitions any Sacała’s line defines a wide class of related quasibranching processes which are more general than Markov processes. Didactically such an approach is extremely useful.