SYMMETRIC MENDELSOHN TRIPLE SYSTEM AND LARGE SETS OF DISJOINT MENDELSOHN TRIPLE SYSTEMS

For an MTS(v)=(S,(?)), if there exists a,b∈S(a≠b) such that 〈a, b, x〉∈(?)〈b,a,x〉∈(?) and 〈a,x,y〉∈(?)〈b,y,x〉∈(?)(x,y∈S\{a,b}) then we call MTS(v) a symmetric Mendelsohn triple system of order v and denote it by SMTS(v). If there exist (v—2) MTS(v)s which are pairwise disjoint (or SMTS(v))