We 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. © Springer-Verlag Berlin Heidelberg 2007.
CITATION STYLE
Chifman, J., & Petrović, S. (2007). Toric ideals of phylogenetic invariants for the general group-based model on claw trees K1,n. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 4545 LNCS, pp. 307–321). Springer Verlag. https://doi.org/10.1007/978-3-540-73433-8_22
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