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

✍ Scribed by G.K. Bennett; M.J. Grannell; T.S. Griggs

Publisher
Elsevier Science
Year
2002
Tongue
English
Weight
57 KB
Volume
23
Category
Article
ISSN
0195-6698

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✦ Synopsis

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 order n, 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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