On the bi-embeddability of certain Steiner triple systems of order 15

Bennett, G.K.; Grannell, M.J. and Griggs, T.S. (2002). On the bi-embeddability of certain Steiner triple systems of order 15. European Journal of Combinatorics, 23(5) pp. 499–505.

DOI: https://doi.org/10.1006/eujc.2002.0559

Abstract

There are 80 non-isomorphic Steiner triple systems of order 15. A standard listing of these is given in Mathon et al.(1983, Ars Combin., 15, 3–110). We prove that systems #1 and #2 have no bi-embedding together in an orientable surface. This is the first known example of a pair of Steiner triple systems of ordern , satisfying the admissibility condition n ≡ 3 or 7(mod 12), which admits no orientable bi-embedding. We also show that the same pair has five non-isomorphic bi-embeddings in a non-orientable surface.