On the number of maximum genus embeddings of almost all graphs (Q1193548)

By performing an induction in the context of permutation-partition pairs, the author obtains a lower bound for the number of orientable maximum genus labelled 2-cell imbeddings of almost all graphs. He shows that, although the bound is far from sharp, it is sufficiently strong to establish that for complete graphs triangulating an orientable surface the number of maximum genus imbeddings far exceeds the number of minimum genus imbeddings.