Minimal decompositions of hypergraphs into mutually isomorphic subhypergraphs (Q1168335)

The authors tackle the following problem: given a family\(\{H_1,\dots,H_k\}\) of \(r\)-uniform hypergraphs, each with the same number of edges, find the smallest \(t\) such that each \(H_i\) can be decomposed into mutually isomorphic subhypergraphs \(E_{ij},1\leq j\leq t\). This study extends the authors' previous work on the case \(r=2\) [Combinatorica 1, 13-24 (1981)]. The main techniques used are interesting counting arguments. The results obtained are good but not sharp, so many open problems remain.