On large sets of resolvable and almost resolvable oriented triple systems

An MTS(v) or DTS(v)] is said to be resolvable, denoted by RMTS(v) or RDTS(v)], if its block set can be partitioned into parallel classes. An MTS(v) or DTS(v)] is said to be almost resolvable, denoted by ARMTS(v) or ARDTS(v)], if its block set can be partitioned into almost parallel classes. The large set of RMTS(v) or RDTS(v) or ARMTS(v) or ARDTS(v)] is denoted by LRMTS(v) or LRDTS(v) or LARMTS(v) or LARDTS(v)]. In this article we do some preliminary study for their existence, and give several recursive theorems using other combinatorial structures. © 1996 John Wiley & Sons, Inc.