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TitleToric ideals of phylogenetic invariants for the general group-based model on claw trees $K_1,n $.
Author(s) Julia Chifman, Sonja Petrovic
TypeBook, Chapter in Book, Conference Proceeding
AbstractWe address the problem of studying the toric ideals of phylogenetic invariants for a general group-based model on an arbitrary claw tree. We focus on the group ℤ2 and choose a natural recursive approach that extends to other groups. The study of the lattice associated with each phylogenetic ideal produces a list of circuits that generate the corresponding lattice basis ideal. In addition, we describe explicitly a quadratic lexicographic Gröbner basis of the toric ideal of invariants for the claw tree on an arbitrary number of leaves. Combined with a result of Sturmfels and Sullivant, this implies that the phylogenetic ideal of every tree for the group ℤ2 has a quadratic Gröbner basis. Hence, the coordinate ring of the toric variety is a Koszul algebra.
ISBN978-3-540-73432-1/pbk
URL http://link.springer.com/chapter/10.1007%2F978-3-540-73433-8_22
LanguageEnglish
Pages307--321
PublisherBerlin: Springer
Year2007
Edition0
Translation No
Refereed No
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