  The interstellar medium of low-metallicity systems undergoing star formation
will show chemical abundance inhomogeneities due to supernova events enriching
the medium on a local scale. If the star formation time-scale is shorter than
the time-scale of mixing of the interstellar matter, the inhomogeneities are
reflected in the surface abundances of low-mass stars and thereby detailed
information on the nucleosynthesis in the first generations of supernovae is
preserved. Characteristic patterns and substructures are therefore expected to
be found, apart from the large scatter behaviour, in the distributions of stars
when displayed in diagrams relating different element abundance ratios. These
patterns emerge from specific variations with progenitor stellar mass of the
supernova yields and it is demonstrated that the patterns are insensitive to
the initial mass function (IMF) even though the relative density of stars
within the patterns may vary. An analytical theory of the formation of patterns
is presented and it is shown that from a statistical point of view the
abundance ratios can trace the different nucleosynthesis sites even when mixing
of the interstellar medium occurs. Using these results, it should be possible
to empirically determine supernova yields from the information on relative
abundance ratios of a large, homogeneous sample of extremely metal-poor
Galactic halo stars.
