Generating functions for multi-labeled trees
type: Item
instance of: scholarly article
title: Generating functions for multi-labeled trees
zbMATH Open document ID: 1255.05044
author: Éva Czabarka
author: Péter L. Erdős
author: Virginia Johnson
author: Vincent Moulton
published in: Discrete Applied Mathematics
publication date: 2012-11-22T00:00:00Z
review text: 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.
reviewed by: William G. Brown
Mathematics Subject Classification ID: 05C05
Mathematics Subject Classification ID: 05C30
Mathematics Subject Classification ID: 92D10
zbMATH DE Number: 6109936
zbMATH Keywords: phylogenetic tree
zbMATH Keywords: multi-labeled tree
zbMATH Keywords: MUL-tree
zbMATH Keywords: generating function
MaRDI profile type: Publication
full work available at URL: j.dam.2012.08.010
OpenAlex ID: W1993799876
Wikidata QID: Q41455295
DBLP publication ID: journals/dam/CzabarkaEJM13
DOI: 10.1016/J.DAM.2012.08.010
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description: scientific article; zbMATH DE number 6109936