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, 1972•cambridge.orgWe 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.
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