Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: 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).  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.  also show that the same pair has five non-isomorphic bi-embeddings in a non-orientable surface.
['G. K. Bennett', 'Mike J. Grannell', 'Terry S. Griggs']
I am writing a research paper on a idea On the Bi-embeddability of Certain Steiner Triple Systems of Order 15
[{"from": "human", "value": "I am writing a research paper on a idea On the Bi-embeddability of Certain Steiner Triple Systems of Order 15"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: 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).  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.  also show that the same pair has five non-isomorphic bi-embeddings in a non-orientable surface."}]