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Cyclic bi-embeddings of Steiner triple systems on 31 points

Published online by Cambridge University Press:  04 June 2001

G. K. Bennett ,
M. J. Grannell  and
T. S. Griggs
G. K. Bennett
Affiliation:
Department of Pure Mathematics, The Open University, Walton Hall, Milton Keynes MK7 6AA, United Kingdom e-mail:gkb53@hotmail.com, m.j.grannell@open.ac.uk, t.s.griggs@open.ac.uk
M. J. Grannell
Affiliation:
Department of Pure Mathematics, The Open University, Walton Hall, Milton Keynes MK7 6AA, United Kingdom e-mail:gkb53@hotmail.com, m.j.grannell@open.ac.uk, t.s.griggs@open.ac.uk
T. S. Griggs
Affiliation:
Department of Pure Mathematics, The Open University, Walton Hall, Milton Keynes MK7 6AA, United Kingdom e-mail:gkb53@hotmail.com, m.j.grannell@open.ac.uk, t.s.griggs@open.ac.uk
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We investigate cyclic bi-embeddings in an orientable surface of Steiner triple systems on 31 points. Up to isomorphism, we show that there are precisely 2408 such embeddings. The relationship of these to solutions of Heffter's first difference problem is discussed and a procedure described which, under certain conditions, transforms one bi-embedding to another.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 43 , Issue 1 , January 2001 , pp. 145 - 151
Copyright
2001 Glasgow Mathematical Journal Trust