Explicit Baranyai partitions for quadruples, Part I: Quadrupling constructions

It is well known that, whenever k divides n, the complete k-uniform hypergraph on n vertices can be partitioned into disjoint perfect matchings. Equivalently, set of k-subsets an n-set parallel classes so that each class a partition n-set. This result as Baranyai's theorem, which guarantees existence Baranyai partitions. Unfortunately, proof theorem uses network flow arguments, making this nonexplicit. In particular, there no method to produce partitions in time and space scale linearly with number hyperedges hypergraph. desirable for certain applications have explicit construction generates linear time. Such efficient = 2 3. paper, we present recursive quadrupling 4 t, where t ≡ 0 , 3 6 8 9 ( mod 12 ) . follow-up paper (Part II), other values namely, 1 5 7 10 11 will considered.