# Leaf multiplicity in a Bienaymé-Galton-Watson tree

@article{Brandenberger2021LeafMI, title={Leaf multiplicity in a Bienaym{\'e}-Galton-Watson tree}, author={Anna M. Brandenberger and Luc Devroye and Marcel K. Goh and Rosie Y. Zhao}, journal={Discret. Math. Theor. Comput. Sci.}, year={2021}, volume={24} }

This note defines a notion of multiplicity for nodes in a rooted tree and
presents an asymptotic calculation of the maximum multiplicity over all leaves
in a Bienaym\'e-Galton-Watson tree with critical offspring distribution $\xi$,
conditioned on the tree being of size $n$. In particular, we show that if $S_n$
is the maximum multiplicity in a conditional Bienaym\'e-Galton-Watson tree,
then $S_n = \Omega(\log n)$ asymptotically in probability and under the further
assumption that ${\bf E}\{2^\xi…

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