Combinatorial characterization of a certain class of words and a conjectured connection with general subclasses of phylogenetic tree-child networks.

ABSTRACT: The combinatorial study of phylogenetic networks has attracted much attention in recent times. In particular, one class of them, the so-called tree-child networks, are becoming the most prominent ones. However, their combinatorial properties are largely unknown. In this paper we address the problem of exactly counting them. We conjecture a relationship with the cardinality of a certain class of words. By solving the counting problem for the words, and on the basis of the conjecture, several simple recurrence formulas for general cases arise. Moreover, a precise asymptotic analysis is provided. Our results coincide with all current formulas in the literature for particular subclasses of tree-child networks, as well as with numerical results obtained for small networks. We expect that the st

SUBMITTER: Pons M 

PROVIDER: S-EPMC8575882 | biostudies-literature | 2021 Nov

REPOSITORIES: biostudies-literature