1987 Reports

Genus distributions for bouquets of circles

Gross, Jonathan L.; Robbins, David P.; Tucker, Thomas W.

The genus distribution of a graph G is defined to be the sequence {gm} such that gm is the number of different imbeddings of G in the closed orientable surface of genus m. A counting formula of D. M. Jackson concerning the cycle structure of permutations is used to derive the genus distribution for any bouquet of circles Bn. It is proved that all these genus distributions for bouquets are strongly unimodal.