Valency enumeration of rooted plane trees

CL Mallows, KW Wachter - Journal of the Australian Mathematical …, 1972 - cambridge.org
CL Mallows, KW Wachter
Journal of the Australian Mathematical Society, 1972cambridge.org
We obtain the enumerator by node-valencies of planted plane trees, whose square gives the
enumerator of rooted plane trees. We also study the enumeration by number of nodes and
black-node-valencies of bichromatic rooted plane trees, encountering a remarkably simple
inversion formula. Finally, we remark that these bichromatic trees are in 1–1
correspondence with solutions to the weak lead ballot problem.
We obtain the enumerator by node-valencies of planted plane trees, whose square gives the enumerator of rooted plane trees. We also study the enumeration by number of nodes and black-node-valencies of bichromatic rooted plane trees, encountering a remarkably simple inversion formula. Finally, we remark that these bichromatic trees are in 1–1 correspondence with solutions to the weak lead ballot problem.
Cambridge University Press