Balanced P(3)(2,4)-design

Abstract

Given an hypergraph H⁽³⁾ uniform of rank 3, an H⁽³⁾-decomposition of the complete hypergraph K_υ⁽³⁾ is a collection of hypergraphs, all isomorphic to H⁽³⁾ whose edge-sets partition the edge-set of K_υ⁽³⁾, An H⁽³⁾-decomposition of K_υ⁽³⁾ is also called an H(³⁾-design and the hypergraphs of the partition are said to be the blocks. An H⁽³⁾-design is said to be balanced if the number of blocks containing any given vertex of Kv is a constant. In this paper, we determine completely, without exceptions, the spectrum of balanced H⁽³⁾-designs.