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A new existence proof for large sets of disjoint Steiner triple systems
Authors:L Ji
Institution:Department of Mathematics, Suzhou University, Suzhou 215006, China
Abstract:A Steiner triple system of order v (briefly STS(v)) consists of a v-element set X and a collection of 3-element subsets of X, called blocks, such that every pair of distinct points in X is contained in a unique block. A large set of disjoint STS(v) (briefly LSTS(v)) is a partition of all 3-subsets (triples) of X into v-2 STS(v). In 1983–1984, Lu Jiaxi first proved that there exists an LSTS(v) for any v≡1 or with six possible exceptions and a definite exception v=7. In 1989, Teirlinck solved the existence of LSTS(v) for the remaining six orders. Since their proof is very complicated, it is much desired to find a simple proof. For this purpose, we give a new proof which is mainly based on the 3-wise balanced designs and partitionable candelabra systems.
Keywords:Steiner system  Large set  Candelabra system  t-wise balanced design
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