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Non-isomorphic 2-perfect 6-cycle systems of order 13

Published online by Cambridge University Press:  17 April 2009

Rebecca A.H. Gower
Rebecca A.H. Gower
Affiliation:
Department of Mathematics, The University of Queensland, Queensland 4072
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Abstract

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Running a computer search for new, cyclic, 2-perfect 6-cycle systems of order 13 and constructing the quasigroups which arise from such systems enabled the author to establish that there are at most two such non-isomorphic systems. Then by using two-variable laws of the quasigroups it is shown that there are exactly two non-isomorphic 2-perfect 6-cycle systems of order 13 which are cyclic.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 44 , Issue 3 , December 1991 , pp. 381 - 385
Copyright
Copyright © Australian Mathematical Society 1991

References

[1]Gower, R.A.H., Oates-Williams, S., Donovan, D. and Billington, E.J., ‘On the quasigroup variety arising from a 2-perfect 6-cycle system of order 13’, J. Combin. Math. Combin. Comput. (to appear).Google Scholar
[2]Lindner, C.C., Phelps, K.T. and Rodger, C.A., ‘The Spectrum for 2-perfect 6-cycle systems’, J. Combin. Theory A (to appear).Google Scholar
[3]Lindner, C.C., ‘Graph decompositions and quasigroup identities’, in Proceedings of the Second International Catania Combinatorial Conference, “Graphs, designs and combinatorial geometries” (Universita di Catania, Catania, Sicily, 1989 to appear).Google Scholar