Self-converse large sets of pure hybrid triple systems

Abstract

A hybrid triple system of order v, briefly by HTS (v), is a pair (X, B) where X is a v-set and B is a collection of cyclic and transitive triples (called blocks) on X such that every ordered pair of X belongs to exactly one block of B. An HTS (v) is called pure and denoted by PHTS (v) if one element of the block set {(x, y, z), (z, y, x), (z, x, y), (y, x, z), (y, z, x), (x, z, y), 〈x, y, z〉, 〈z, y, x〉} is contained in B then the others will not be contained in B. A self-converse large set of disjoint PHTS (v)s, denoted by LPHTS*(v), is a collection of 4(v − 2) disjoint PHTS (v)s which contains exactly (v − 2)/2 converse octads of PHTS (v)s. In this paper, some results about the existence for LPHTS*(v) are obtained.