Kirkman triple systems of order 21 with nontrivial automorphism group

被引：0

作者：

Cohen, MB ^{[1
]}

Colbourn, CJ

Ives, LA

Ling, ACH

机构：

[1] Univ Auckland, Dept Comp Sci, Auckland, New Zealand

[2] Arizona State Univ, Dept Comp Sci & Engn, Tempe, AZ 85287 USA

[3] Univ Vermont, Dept Math & Stat, Burlington, VT 05405 USA

[4] Univ Vermont, Dept Comp Sci, Burlington, VT 05405 USA

来源：

MATHEMATICS OF COMPUTATION | 2002年 / 71卷 / 238期

关键词：

Kirkman triple system; doubly resolvable design; Steiner triple system; constructive enumeration;

D O I：

暂无

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

There are 50,024 Kirkman triple systems of order 21 admitting an automorphism of order 2. There are 13,280 Kirkman triple systems of order 21 admitting an automorphism of order 3. Together with the 192 known systems and some simple exchange operations, this leads to a collection of 63,745 nonisomorphic Kirkman triple systems of order 21. This includes all KTS(21)s having a nontrivial automorphism group. None of these is doubly resolvable. Four are quadrilateral-free, providing the first examples of such a KTS(21).

引用

页码：873 / 881

页数：9

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