On the Bi-embeddability of Certain Steiner Triple Systems of Order 15

Department of Pure Mathematics, The Open University, Walton Hall, Milton Keynes, MK7 6AA, .ukf1
European Journal of Combinatorics (Impact Factor: 0.65). 07/2002; 23(5):499-505. DOI: 10.1006/eujc.2002.0559
Source: OAI


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.

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