| Institution: | Department of Computer Science, University of Auckland, Auckland, New Zealand ; Department of Computer Science and Engineering, Arizona State University, Tempe, Arizona 85287-5406 ; Department of Mathematics and Statistics, University of Vermont, Burlington, Vermont 05405 Alan C. H. Ling ; Department of Computer Science, University of Vermont, Burlington, Vermont 05405 |
| Abstract: | 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). |
