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Kirkman triple systems of order 21 with nontrivial automorphism group


Authors: Myra B. Cohen, Charles J. Colbourn, Lee A. Ives and Alan C. H. Ling
Journal: Math. Comp. 71 (2002), 873-881
MSC (2000): Primary 05B07
DOI: https://doi.org/10.1090/S0025-5718-01-01372-2
Published electronically: November 21, 2001
MathSciNet review: 1885635
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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).


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Additional Information

Myra B. Cohen
Affiliation: Department of Computer Science, University of Auckland, Auckland, New Zealand
Email: myra@cs.auckland.ac.nz

Charles J. Colbourn
Affiliation: Department of Computer Science and Engineering, Arizona State University, Tempe, Arizona 85287-5406
Email: Charles.Colbourn@asu.edu

Lee A. Ives
Affiliation: Department of Mathematics and Statistics, University of Vermont, Burlington, Vermont 05405

Alan C. H. Ling
Affiliation: Department of Computer Science, University of Vermont, Burlington, Vermont 05405
Email: aling@emba.uvm.edu

DOI: https://doi.org/10.1090/S0025-5718-01-01372-2
Keywords: Kirkman triple system, doubly resolvable design, Steiner triple system, constructive enumeration
Received by editor(s): May 30, 2000
Received by editor(s) in revised form: August 14, 2000
Published electronically: November 21, 2001
Article copyright: © Copyright 2001 American Mathematical Society