On large sets of hybrid triple systems
An oriented triple system \(\mathcal B\) on a \(v\)-set \(X\) is called a hybrid triple system and denoted by \(\text{HTS}(v, \lambda)\) if it contains both cyclic and transitive triples such that each ordered pair of distinct elements is contained in exactly \(\lambda\) triples of \(\mathcal B\). If all the cyclic and transitive triples from \(X\) can be partitioned into \(\bigcup_i {\mathcal B}_i\) such that each \((X, {\mathcal B}_i)\) is an \(\text{HTS}(v, \lambda)\), then \(\{(X, {\mathcal B}_i)\}_i\) is called a large set of pairwise disjoint hybrid triple systems and denoted by \(\text{LHKTS}(v, \lambda)\). In this paper, the authors determine necessary and sufficient conditions for the existence of \(\text{LHKTS}(v, \lambda)\).
scientific article; zbMATH DE number 906656