Gorenstein property for phylogenetic trivalent trees

Low degree minimal generators of phylogenetic semigroups

The phylogenetic semigroup on a graph generalizes the Jukes-Cantor binary model on a tree. Minimal generating sets of phylogenetic semigroups have been described for trivalent trees by Buczyńska and Wiśniewski, and for trivalent graphs with first Betti number 1 by Buczyńska. We characterize degree two minimal generators of the phylogenetic semigroup on any trivalent graph. Moreover, for any graph with first Betti number 1 and for any trivalent graph with first Betti number 2 we describe the minimal generating set of its phylogenetic semigroup.

三脚架的正常系统发育簇的分类

Classification of normal phylogenetic varieties for tripods

本文完整分类了源自三脚架及三价树的正常系统发育簇，并证明基于群的系统发育簇 $X_{G,\mathcal{T}}$ 射影正常当且仅当 $G$ 属于特定的6个阿贝尔群之一。

The Edge-Product Space of Phylogenetic Trees is Not Shellable

The edge-product space of phylogenetic trees is a regular CW complex whose maximal closed cells correspond to trivalent trees with leaves labeled by a finite set $X$. The face poset of this cell decomposition is isomorphic to the Tuffley poset, a poset of labeled forests, with a unique minimum adjoined. We show that the edge-product space of phylogenetic trees is gallery-connected. We then use combinatorial properties of the Tuffley poset and a related graph known as NNI-tree space to show that, although open intervals of the Tuffley poset were proven to be shellable by Gill, Linusson, Moulton…