Self-embeddings of doubled affine Steiner triple systems
نویسندگان
چکیده
Given a properly face two-coloured triangulation of the graph Kn in a surface, a Steiner triple system can be constructed from each of the colour classes. The two Steiner triple systems obtained in this manner are said to form a biembedding. If the systems are isomorphic to each other it is a self-embedding. In the following, for each k ≥ 2, we construct a self-embedding of the doubled affine Steiner triple system AG(k, 3) in a nonorientable surface. We also make use of a construction due to Grannell, Griggs and Širáň to obtain a biembedding of AG(k, 3) in a nonorientable surface that is not a self-embedding for k > 2.
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عنوان ژورنال:
- Australasian J. Combinatorics
دوره 66 شماره
صفحات -
تاریخ انتشار 2016