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 | References | Similar Articles | Additional Information

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