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Title: Counting phylogenetic networks with few reticulation vertices: exact enumeration and corrections
Authors: 符麥克
Fuchs, Michael
Gittenberger, Bernhard
Mansouri, Marefatollah
Contributors: 應數系
Date: 2021-03
Issue Date: 2022-02-10 14:59:15 (UTC+8)
Abstract: In previous work, we gave asymptotic counting results for the number of tree-child and normal networks with k reticulation vertices and explicit exponential generating functions of the counting sequences for k=1,2,3. The purpose of this note is two-fold. First, we make some corrections to our previous approach which overcounted the above numbers and thus gives erroneous exponential generating functions (however, the overcounting does not effect our asymptotic counting results). Secondly, we use our (corrected) exponential generating functions to derive explicit formulas for the number of tree-child and normal networks with k=1,2,3 reticulation vertices. This re-derives recent results of Carona and Zhang, answers their question for normal networks with k=2, and adds new formulas in the case k=3.
Relation: Australas. J. Combin., Vol.81, No.2, pp.257-282
Data Type: article
Appears in Collections:[應用數學系] 期刊論文

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