H-Representation of the Kimura-3 Polytope

Abstract

Given a group-based Markov model on a tree, one can compute the vertex representation of a polytope which describes the associated toric variety. The half-space representation, however, is not easily computable. In the case of ${\mathbb{Z}}_2$ or ${\mathbb{Z}}_2\times {\mathbb{Z}}_2$, these polytopes have applications in the field of phylogenetics. We provide a half-space representation for the $m$-claw tree where $G={\mathbb{Z}}_2\times {\mathbb{Z}}_2$, which corresponds to the Kimura-3 model of evolution.

12 pages

References in corpus (2)

• Invariant versus classical quartet inference when evolution is heterogeneous across sites and lineages
• Identifiability of 3-Class Jukes-Cantor Mixtures

Cited by in corpus (1)

• Finite phylogenetic complexity of $Z_p$ and invariants for $Z_3$