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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 Journal of Combinatorics, Vol.93, 103278
Data Type:	article
DOI link:	https://doi.org/10.1016/j.ejc.2020.103278
DOI:	10.1016/j.ejc.2020.103278
Appears in Collections:	[Department of Mathematical Sciences] Periodical Articles

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