Generating functions for multi-labeled trees
A tree is \textit{leaf-labelled} or \textit{phylogenetic} if each of its vertices of degree 1 (leaves) is labelled by precisely one element from a fixed set of \textit{labels} (which correspond to the species, populations or organisms under consideration,) \textit{and if no label is used more than once}. (The authors' definition differs from that of their cited reference [\textit{C. Semple} and \textit{M. Steel}, Phylogenetics. Oxford: Oxford University Press (2003; Zbl 1043.92026)].) In a \textit{leaf-multi-labelled} tree or MUL-tree [\textit{K. T. Huber} and \textit{V. Moulton}, J.\ Math.\ Biol.\ 52, No.\ 5, 613--632 (2006; Zbl 1110.92027)] the same label may be used on more than one leaf. In this paper the authors ``derive formulæ for generating functions enumerating leaf-multi-labeled trees and use these to derive recursions for counting such trees'' (from their abstract). In particular, they generalize work of \textit{E.\ F.\ Harding} [Adv.\ Appl.\ Probab.\ 3, 44--77 (1971; Zbl 0241.92012)], and of R. Otter.
scientific article; zbMATH DE number 6109936
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