Distance and fractional isomorphism in Steiner triple systems

Distance and fractional isomorphism in Steiner triple systems

A.D. Forbes, M.J. Grannell and T.S. Griggs Department of Mathematics The Open University Walton Hall, Milton Keynes MK7 6AA UNITED KINGDOM [email protected] [email protected] [email protected] Abstract In [8], Quattrochi and Rinaldi introduced the idea of n−1 isomorphism between Steiner systems. In this paper we study this concept in the context of Steiner triple systems. Th...

Bicoloring Steiner Triple Systems

A Steiner triple system has a bicoloring with m color classes if the points are partitioned into m subsets and the three points in every block are contained in exactly two of the color classes. In this paper we give necessary conditions for the existence of a bicoloring with 3 color classes and give a multiplication theorem for Steiner triple systems with 3 color classes. We also examine bicolo...

Balanced Steiner Triple Systems

A Steiner triple system of order v (briefly STS(v)) is a pair (X, B), where X is a v-element set and B is a collection of 3-subsets of X (triples), such that every pair of X is contained in exactly one triple of B. It is well known that a necessary and sufficient condition for a STS(v) to exist is that v#1 or 3 (mod 6). An r-coloring of a STS(v) is a map , : X [1, ..., r] such that at least two...

Configurations in Steiner triple systems

" Combinatorial Designs and their Applications " c 1999 (copyright owner as specified in the book).

Embedding Steiner triple systems in hexagon triple systems