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https://ah.nccu.edu.tw/handle/140.119/139047
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| Title: | On the asymptotic growth of the number of tree-child networks |
| Authors: | 符麥克 Fuchs, Michael Yu, Guan-Ru Zhang, Louxin |
| Contributors: | 應數系 |
| Date: | 2021-03 |
| Issue Date: | 2022-02-10 14:59:42 (UTC+8) |
| Abstract: | In a recent paper, McDiarmid, Semple, and Welsh (2015) showed that the number of tree-child networks with n leaves has the factor n^2n in its main asymptotic growth term. In this paper, we improve this by completely identifying the main asymptotic growth term up to a constant. More precisely, we show that the number of tree-child networks with n leaves grows like where a1=-2.338107410... is the largest root of the Airy function of the first kind. For the proof, we bijectively map the underlying graph-theoretical problem onto a problem on words. For the latter, we can find a recurrence to which a recent powerful asymptotic method of Elvey Price, Fang, and Wallner (2019) can be applied. |
| Relation: | European J. Combin., Vol.93, pp.103278 |
| Data Type: | article |
| DOI 連結: | https://doi.org/10.1016/j.ejc.2020.103278 |
| Appears in Collections: | [應用數學系] 期刊論文 |
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