Year: 2026
Type: preprint
Abstract: Tree-child networks are a useful class of binary phylogenetic networks. The Pons--Batle identity (Pons and Batle, \textit{Scientific Reports}, 2021) states that the number $a_{n,k}$ of tree-child networks with $k$ reticulations on $n$ taxa satisfies \[ a_{n,k}=(n-k+1)a_{n,k-1} +\frac{n(2n+k-3)}{n-k}a_{n-1,k}. \] In this paper, we present a short combinatorial proof of this identity.
Source: arXiv (Cornell University)
Authors: Yu, Hao, Zhang, Louxin
Institution: National University of Singapore
Language: English
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Funder: Ministry of Education, India
OpenAlex ID: W7211879296