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The maximum independence number of Steiner triple systems of order v is well‐known. Motivated by questions of access balancing in storage systems, we determine the maximum total cardinality of a pair of disjoint independent sets of Steiner triple systems of order v for all admissible orders. [ABSTRACT FROM AUTHOR]

A classical construction of Bose produces a Steiner triple system of order 3 n from a symmetric, idempotent latin square of order n , which exists whenever n is odd. In an application to access-balancing in storage systems, certain Bose triple systems play a central role. A natural question arises: For which orders v does there exist a resolvable Bose triple system? Elementary counting establishes the necessary condition that v ≡ 9 (mod 18). For specific Bose triple systems that optimize an access metric, we show that v ≡ 9 (mod 18) is also sufficient. [ABSTRACT FROM AUTHOR]

Abstract: A Hanani triple system of order , , is a decomposition of the complete graph into sets of disjoint triangles and one set of disjoint triangles. A nearly Kirkman triple system of order , , is a decomposition of into sets of disjoint triangles; here is a one-factor of . The Hanani triple systems of order and the nearly Kirkman triple systems of order can be classified using the classification of the Steiner triple systems of order . This is carried out here for : There are 3787983639 isomorphism classes of s and 25328 isomorphism classes of s. Several properties of the classified systems are tabulated. In particular, seven of the s have orthogonal resolutions, and five of the s admit a pair of resolutions in which the almost parallel classes are orthogonal. [Copyright &y& Elsevier]

Abstract: A -design on points embeds a Steiner triple system (STS) if there is a subset of points on which the graphs of the design induce the blocks of a STS. It is established that , and that when equality is met that such a minimum embedding of an exists, except when . [Copyright &y& Elsevier]

Steiner triple systems are well studied combinatorial designs that have been shown to possess properties desirable for the construction of multiple erasure codes in RAID architectures. The ordering of the columns in the parity check matrices of these codes affects system performance. Combinatorial problems involved in the generation of good and bad column orderings are defined, and examined for small numbers of accesses to consecutive data blocks in the disk array. [Copyright &y& Elsevier]