In either string or independent fragmentation, an iterative approach is used to describe the fragmentation process. Given an initial quark , it is assumed that a new pair may be created, such that a meson is formed, and a is left behind. This may at a later stage pair off with a , and so on. What need be given is thus the relative probabilities to produce the various possible pairs, , , , etc., and the relative probabilities that a given quark pair combination forms a specific meson, e.g. for either , or some higher state.
In PYTHIA, to first approximation it is assumed that the two aspects can be factorized, i.e. that it is possible first to select a pair, without any reference to allowed physical meson states, and that, once the flavour combination is given, it can be assigned to a given meson state with total probability unity. Corrections to this factorized ansatz will come especially in the baryon sector.