Kirkman triple systems of order 21 with nontrivial automorphism group
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- by Myra B. Cohen, Charles J. Colbourn, Lee A. Ives and Alan C. H. Ling PDF
- Math. Comp. 71 (2002), 873-881 Request permission
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).References
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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
- Received by editor(s): May 30, 2000
- Received by editor(s) in revised form: August 14, 2000
- Published electronically: November 21, 2001
- © Copyright 2001 American Mathematical Society
- Journal: Math. Comp. 71 (2002), 873-881
- MSC (2000): Primary 05B07
- DOI: https://doi.org/10.1090/S0025-5718-01-01372-2
- MathSciNet review: 1885635