Enumeration of d-combining Tree-Child Networks

2022/03/15 by Yu-Sheng Chang, Chang, Yu-Sheng, Michael Fuchs +7
Mathematics · #05C20 #60C05 #60F05 #92D15 #Combinatorics (math.CO) #FOS: Mathematics #math.CO #msc:05C20 #msc:60C05 #msc:60F05 #msc:92D15

paper · pdf · doi:10.48550/arxiv.2203.07619

Extended abstract which is accepted for presentation at AofA2022; an accompanying Maple worksheet can be found in the ancillary file folder

arxiv created 2022/03/15 · arxiv updated 2022/03/16

Abstract

Tree-child networks are one of the most prominent network classes for modeling evolutionary processes which contain reticulation events. Several recent studies have addressed counting questions for \it bicombining tree-child networks which are tree-child networks with every reticulation node having exactly two parents. In this paper, we extend these studies to \it d-combining tree-child networks where every reticulation node has now d≥ 2 parents. Moreover, we also give results and conjectures on the distributional behavior of the number of reticulation nodes of a network which is drawn uniformly at random from the set of all tree-child networks with the same number of leaves.

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