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    題名: On the asymptotic growth of the number of tree-child networks
    作者: 符麥克
    Fuchs, Michael
    Yu, Guan-Ru
    Zhang, Louxin
    貢獻者: 應數系
    日期: 2021-03
    上傳時間: 2022-02-10 14:59:42 (UTC+8)
    摘要: 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.
    關聯: European Journal of Combinatorics, Vol.93, 103278
    資料類型: article
    DOI 連結: https://doi.org/10.1016/j.ejc.2020.103278
    DOI: 10.1016/j.ejc.2020.103278
    顯示於類別:[應用數學系] 期刊論文

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