Resolving triple systems into regular configurations (Q1964485)

A configuration in a triple system is a set of triples. It is regular when every element of the triple system appearing in some triple of the configuration appears in exactly \(p\) such triples, for \(p\) a constant independent of the element chosen. A resolution of a triple system into a regular configuration \(C\) is a partition of the triples into isomorphic copies of \(C\), along with a partition of these copies into classes so that each class consists of element-disjoint copies of \(C\) which together contain all elements of the triple system. Resolutions of triple systems into regular configurations having six or fewer triples are examined, and a complete characterization is given when the configuration has four or fewer triples.