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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