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https://ah.lib.nccu.edu.tw/handle/140.119/139045
題名: | Counting phylogenetic networks with few reticulation vertices: exact enumeration and corrections | 作者: | 符麥克 Fuchs, Michael Gittenberger, Bernhard Mansouri, Marefatollah |
貢獻者: | 應數系 | 日期: | Mar-2021 | 上傳時間: | 10-Feb-2022 | 摘要: | 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. | 關聯: | Australas. J. Combin., Vol.81, No.2, pp.257-282 | 資料類型: | article |
Appears in Collections: | 期刊論文 |
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