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Exact Enumeration of Phylogenetic Networks: The Tree-Child, Reticulation-Visible and Orchard Hierarchy
We develop a unified framework for the exact enumeration and asymptotic analysis of the three most studied classes of phylogenetic networks: tree-child (TC), reticulation-visible (RV) and orchard networks, whose cardinalities satisfy the strict ordering $|\mathrm{TC}_{\ell,k}|<|\mathrm{RV}_{\ell,k}|
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