Geodesic
On the number of vertices of each rank in phylogenetic trees and their generalizations
Discrete mathematics & theoretical computer science, Tome 18 (2015-2016) no. 3.

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We find surprisingly simple formulas for the limiting probability that the rank of a randomly selected vertex in a randomly selected phylogenetic tree or generalized phylogenetic tree is a given integer. 
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Bóna, Miklós. On the number of vertices of each rank in phylogenetic trees and their generalizations. Discrete mathematics & theoretical computer science, Tome 18 (2015-2016) no. 3. doi : 10.46298/dmtcs.653. http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.653/

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