(1,2)-Resolvable candelabra quadruple systems and Steiner quadruple systems

摘要

(1,α)-resolvable candelabra quadruple systems play an important role in the construction of (1,α)-resolvable Steiner quadruple systems. In this paper, we consider (1,2)-resolvable candelabra quadruple systems with three groups and show that the necessary conditions on the existence of (1,2)-RCQS(~(g3):s) when g is even are also sufficient. As its application, we improve the existing result on (1,2)-resolvable Steiner quadruple systems.