On 6-sparse Steiner triple systems

被引:26
作者
Forbes, A. D. [1 ]
Grannell, M. J. [1 ]
Griggs, T. S. [1 ]
机构
[1] Open Univ, Dept Pure Math, Milton Keynes MK7 6AA, Bucks, England
关键词
Steiner triple system; k-sparse Steiner triple system; pasch configuration; mitre configuration; crown configuration; perfect steiner triple system;
D O I
10.1016/j.jcta.2006.04.003
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
We give the first known examples of 6-sparse Steiner triple systems by constructing 29 such systems in the residue class 7 modulo 12, with orders ranging from 139 to 4447. We then present a recursive construction which establishes the existence of 6-sparse systems for an infinite set of orders. Observations are also made concerning existing construction methods for perfect Steiner triple systems, and we give a further example of such a system. This has order 135,859 and is only the fourteenth known. Finally, we present a uniform Steiner triple system of order 180,907. (c) 2006 Elsevier Inc. All rights reserved.
引用
收藏
页码:235 / 252
页数:18
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