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  1. Aims. Various nucleosynthesis studies have pointed out that the r -process elements in very metal-poor (VMP) halo stars might have different origins. By means of familiar concepts from statistics (correlations, cluster analysis, and rank tests of elemental abundances), we look for causally correlated elemental abundance patterns and attempt to link them to astrophysical events. Some of these events produce the r -process elements jointly with iron, while others do not have any significant iron contribution. We try to (a) characterize these different types of events by their abundance patterns and (b) identify them among the existing set of suggested r -process sites. Methods. The Pearson and Spearman correlation coefficients were used in order to investigate correlations among r -process elements (X,Y) as well as their relation to iron (Fe) in VMP halo stars. We gradually tracked the evolution of those coefficients in terms of the element enrichments [X/Fe] or [X/Y] and the metallicity [Fe/H]. This approach, aided by cluster analysis to find different structures of abundance patterns and rank tests to identify whether several events contributed to the observed pattern, is new and provides deeper insights into the abundances of VMP stars. Results. In the early stage of our Galaxy, at least three r -process nucleosynthesis sites have been active. The first two produce and eject iron and the majority of the lighter r -process elements. We assign them to two different types of core-collapse events, not identical to regular core-collapse supernovae (CCSNe), which produce only light trans-Fe elements. The third category is characterized by a strong r -process and is responsible for the major fraction of the heavy main r -process elements without a significant coproduction of Fe. It does not appear to be connected to CCSNe, in fact most of the Fe found in the related r -process enriched stars must come from previously occurring CCSNe. The existence of actinide boost stars indicates a further division among strong r -process sites. We assign these two strong r -process sites to neutron star mergers without fast black hole formation and to events where the ejecta are dominated by black hole accretion disk outflows. Indications from the lowest-metallicity stars hint at a connection with massive single stars (collapsars) forming black holes in the early Galaxy. 
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