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Markov invariants and the isotropy subgroup of a quartet tree
journal contribution
posted on 2023-05-17, 01:22 authored by Jeremy SumnerJeremy Sumner, Peter JarvisPeter JarvisThe purpose of this article is to show how the isotropy subgroup of leaf permutations on binary trees can be used to systematically identify tree-informative invariants relevant to models of phylogenetic evolution. In the quartet case, we give an explicit construction of the full set of representations and describe their properties. We apply these results directly to Markov invariants, thereby extending previous theoretical results by systematically identifying linear combinations that vanish for a given quartet. We also note that the theory is fully generalizable to arbitrary trees and is equally applicable to the related case of phylogenetic invariants. All results follow from elementary consideration of the representation theory of finite groups.
History
Publication title
Journal of Theoretical BiologyVolume
258Pagination
302-310ISSN
0022-5193Department/School
School of Natural SciencesPublisher
Academic Press Ltd-Elsevier Science LtdPlace of publication
London, EnglandRights statement
The definitive version is available at http://www.sciencedirect.comRepository Status
- Restricted