A new existence proof for large sets of disjoint Steiner triple systems

作者：Ji L^*

来源：Journal of Combinatorial Theory - Series A, 2005, 112(2): 308-327.

DOI：10.1016/j.jcta.2005.06.005

• Steiner system
• large set
• Candelabra system
• t-wise balanced design

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 3 (mod 6) 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.

• 出版日期2005-11
• 单位苏州大学; 宿州学院