Combinatorics of non-ambiguous trees

Combinatorics of non - ambiguous trees † ‡

This article investigates combinatorial properties of non-ambiguous trees. These objects we define may be seen either as binary trees drawn on a grid with some constraints, or as a subset of the tree-like tableaux previously defined by Aval, Boussicault and Nadeau. The enumeration of non-ambiguous trees satisfying some additional constraints allows us to give elegant combinatorial proofs of ide...

Combinatorics of least-squares trees.

A recurring theme in the least-squares approach to phylogenetics has been the discovery of elegant combinatorial formulas for the least-squares estimates of edge lengths. These formulas have proved useful for the development of efficient algorithms, and have also been important for understanding connections among popular phylogeny algorithms. For example, the selection criterion of the neighbor...

Combinatorics and Asymptotics on Trees

Combinatorics of Linked Systems of Quartet Trees

We apply classical quartet techniques to the problem of phylogenetic decisiveness and find a value k such that all collections of at least k quartets are decisive. Moreover, we prove that this bound is optimal and give a lower-bound on the probability that a collection of quartets is decisive.

The Combinatorics of Evolutionary Trees—a Survey

We survey here results and problems from the reconstruction theory of evolutionary trees, which involve enumeration and inversion.