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Abstract: A Steiner quadruple system is said to be -resolvable if its blocks can be partitioned into parts such that each point of occurs in exactly two blocks in each part. The necessary condition for the existence of -resolvable Steiner quadruple systems s is or 10 (mod 12). Hartman and Phelps in [A. Hartman, K.T. Phelps, Steiner quadruple systems, in: J.H. Dinitz, D.R. Stinson (Eds.), Contemporary Design Theory, Wiley, New York, 1992, pp. 205–240] posed a question whether the necessary condition for the existence of -resolvable Steiner quadruple systems is sufficient. In this paper, we consider the last twenty orders of -resolvable Steiner quadruple systems and show that the necessary condition for the existence of -resolvable Steiner quadruple systems is also sufficient except for the order 10. [Copyright &y& Elsevier]

Abstract: -resolvable candelabra quadruple systems play an important role in the construction of -resolvable Steiner quadruple systems. In this paper, we consider -resolvable candelabra quadruple systems with three groups and show that the necessary conditions on the existence of -RCQS when is even are also sufficient. As its application, we improve the existing result on -resolvable Steiner quadruple systems. [Copyright &y& Elsevier]

Abstract: It is well known that, given a Steiner triple system, a quasigroup can be formed by defining an operation by the identities and , where is the third point in the block containing the pair . The same is true for a Mendelsohn triple system, where the pair is considered to be ordered. But it is not true in general for directed triple systems. However, directed triple systems which form quasigroups under this operation do exist. We call these Latin directed triple systems, and in this paper we begin the study of their existence and properties. [Copyright &y& Elsevier]

Abstract: A two-fold pentagon system is a decomposition of the complete 2-multigraph (every two distinct vertices joined by two edges) into pentagons. A two-fold Steiner pentagon system is a two-fold pentagon system such that every pair of distinct vertices is joined by a path of length two in exactly two pentagons of the system. We consider two-fold Steiner pentagon systems with an additional property : for any two vertices, the two paths of length two joining them are distinct. We determine completely the spectrum for such systems, and point out an application of such systems to certain 4-cycle systems. [Copyright &y& Elsevier]

We consider the existence problem for 'Steiner networks' (trivalent graphs with 2 π/3 angles at each junction) in strictly convex domains, with 'Neumann' boundary conditions. For each of the three possible combinatorial possibilities, sufficient conditions on the domain are derived for existence. In addition, in each case explicit examples of nonexistence are given. [ABSTRACT FROM AUTHOR]

Abstract: We give a construction of a 2- design starting from a Steiner system and an affine plane of order n. This construction is applied to known classes of Steiner systems arising from affine and projective geometries, Denniston designs, and unitals. We also consider the extendability of these designs to 3-designs. [ABSTRACT FROM AUTHOR]