Glasgow Mathematical Journal



Cyclic bi-embeddings of Steiner triple systems on 31 points


G. K. Bennett a1, M. J. Grannell a1 and T. S. Griggs a1
a1 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

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.

(Received August 27 1999)