Abstract
Orientable triangular embeddings of the complete tripartite graph K n , n , n correspond to biembeddings of Latin squares. We show that if n is prime there are at least e n ln n - n ( 1 + o ( 1 ) ) nonisomorphic biembeddings of cyclic Latin squares of order n. If n = kp , where p is a large prime number, then the number of nonisomorphic biembeddings of cyclic Latin squares of order n is at least e p ln p - p ( 1 + ln k + o ( 1 ) ) . Moreover, we prove that for every n there is a unique regular triangular embedding of K n , n , n in an orientable surface.
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