2 citations · 2 across the 3 of their papers we have counts for
8 papers · 1 filter
Enumeration of -combining Tree-Child Networks
Yu-Sheng Chang, Michael Fuchs, Hexuan Liu +2
Tree-child networks are one of the most prominent network classes for modeling evolutionary processes which contain reticulation events. Several recent studies have addressed count…
Asymptotic Enumeration and Distributional Properties of Galled Networks
Michael Fuchs, Guan-Ru Yu, Louxin Zhang
We show a first-order asymptotics result for the number of galled networks with leaves. This is the first class of phylogenetic networks of {\it large} size for which an asympt…
The distributions under two species-tree models of the number of root ancestral configurations for matching gene trees and species trees
Filippo Disanto, Michael Fuchs, Ariel R. Paningbatan +1
For a pair consisting of a gene tree and a species tree, the ancestral configurations at an internal node of the species tree are the distinct sets of gene lineages that can be pre…
Counting Phylogenetic Networks with Few Reticulation Vertices: Exact Enumeration and Corrections
Michael Fuchs, Bernhard Gittenberger, Marefatollah Mansouri
In previous work, we gave asymptotic counting results for the number of tree-child and normal networks with reticulation vertices and explicit exponential generating functions…
On the Asymptotic Growth of the Number of Tree-Child Networks
Michael Fuchs, Guan-Ru Yu, Louxin Zhang
In a recent paper, McDiarmid, Semple, and Welsh (2015) showed that the number of tree-child networks with leaves has the factor in its main asymptotic growth term. In…
Counting Phylogenetic Networks with Few Reticulation Vertices: Tree-Child and Normal Networks
Michael Fuchs, Bernhard Gittenberger, Marefatollah Mansouri
In recent decades, phylogenetic networks have become a standard tool in modeling evolutionary processes. Nevertheless, basic combinatorial questions about them are still largely op…