Gorenstein property for phylogenetic trivalent trees

Abstract

We study the Gorenstein property for phylogenetic group-based models. We prove that for the groups ${\mathbb{Z}}_3$ and ${\mathbb{Z}}_2\times {\mathbb{Z}}_2$ and trivalent trees the associated polytopes are always Gorenstein extending the results of Buczyńska and Wiśniewski for the group ${\mathbb{Z}}_2$.