Hostname: page-component-cd9895bd7-fscjk Total loading time: 0 Render date: 2025-01-03T17:52:57.819Z Has data issue: false hasContentIssue false
  • English
  • Français

Automorphisms of directed triple systems

Published online by Cambridge University Press:  17 April 2009

Charles J. Colbourn
Charles J. Colbourn
Affiliation:
Department of Combinatorics and Optimization, University of Waterloo, Waterloo, Ontario, CanadaN2L 3G1
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

The obvious necessary conditions for a triple system of index two having a given automorphism group to underly a directed triple system having the same group are shown to be sufficient. An efficient algorithm for directing the triple system in a way that preserves its group is given. Applications to the existence of directed triple systems with various automorphisms are outlined.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 43 , Issue 2 , April 1991 , pp. 257 - 264
Copyright
Copyright © Australian Mathematical Society 1991

References

[1]Cho, C.J., ‘Rotational triple systems’, Ars Combin. 13 (1982), 203–209.Google Scholar
[2]Cho, C.J., Chae, Y. and Hwang, S.G., ‘Rotational directed triple systems’, J. Korean Math. Soc. 24 (1987), 133–142.Google Scholar
[3]Cho, C.J., Han, Y.-H. and Kang, S.-H., ‘Cyclic directed triple systems’, J. Korean Math. Soc. 23 (1986), 117–125.Google Scholar
[4]Colbourn, C.J. and Colbourn, M.J., ‘Every twofold triple system can be directed’, J. Combin. Theory A34 (1983), 375–378.CrossRefGoogle Scholar
[5]Colbourn, C.J. and Harms, J.J., ‘Directing triple systems’, Ars Combin. 15 (1983), 261–266.Google Scholar
[6]Colbourn, M.J. and Colbourn, C.J., ‘Some small directed triple systems’, Congr. Numer. 30 (1981), 247–255.Google Scholar
[7]Colbourn, M.J. and Colbourn, C.J., ‘Cyclic block designs with block size 3’, European J. Combin. 2 (1981), 21–26.CrossRefGoogle Scholar
[8]Colbourn, M.J. and Colbourn, C.J., ‘The analysis of directed triple systems by refinement’, Ann. Discrete Math. 15 (1982), 97–103.Google Scholar
[9]Colbourn, M.J. and Mathon, R.A., ‘On cyclic Steiner 2-designs’, Ann. Discrete Math. 7 (1980), 215–253.CrossRefGoogle Scholar
[10]Doyen, J. and Rosa, A., ‘An updated bibliography on Steiner systems’, Ann. Discrete Math. 7 (1980), 317–349. Unpublished update February, 1989.CrossRefGoogle Scholar
[11]Harms, J.J., ‘Directing cyclic triple systems’, Ann. Discrete Math. 26 (1985), 221–225.Google Scholar
[12]Harms, J.J. and Colbourn, C.J., ‘An optimal algorithm for directing triple systems using eulerian circuits’, Ann. Discrete Math. 27 (1985), 433–438.Google Scholar
[13]Hung, S.H.Y. and Mendelsohn, N.S., ‘Directed triple systems’, J. Combin. Theory A14 (1973), 310–318.CrossRefGoogle Scholar
[14]Seberry, J. and Skillicorn, D., ‘All directed BEBDs with k = 3 exist’, J. Combin. Theory A29 (1980), 244–248.CrossRefGoogle Scholar
[15]Stinson, D.R. and Wallis, W.D., ‘Snappy constructions for triple systems’, Austral. Math. Soc. Gaz. 10 (1983), 84–88.Google Scholar