Abstract

Given a group-based Markov model on a tree, one can compute the vertex representation of a polytope describing a toric variety associated with the algebraic statistical model. In the cases of ${\mathbb Z}_2$ and ${\mathbb Z}_2\times{\mathbb Z}_2$, these polytopes have applications in the field of phylogenetics. We provide a half-space representation of the polytope for the $m$-claw tree where $G={\mathbb Z}_2\times{\mathbb Z}_2$. This choice of group corresponds to the Kimura-3 model of evolution.

Keywords

  1. facet description
  2. polytopes
  3. group-based phylogenetic models

MSC codes

  1. 52B20

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Information & Authors

Information

Published In

cover image SIAM Journal on Discrete Mathematics
SIAM Journal on Discrete Mathematics
Pages: 783 - 795
ISSN (online): 1095-7146

History

Submitted: 10 December 2015
Accepted: 31 January 2017
Published online: 20 April 2017

Keywords

  1. facet description
  2. polytopes
  3. group-based phylogenetic models

MSC codes

  1. 52B20

Authors

Affiliations

Funding Information

National Science Foundation https://doi.org/10.13039/100000001 : DMS-1358534, DMS-1616186

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