Abstract
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.
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Chifman, J., Petrović, S. (2007). Toric Ideals of Phylogenetic Invariants for the General Group-Based Model on Claw Trees K 1,n . In: Anai, H., Horimoto, K., Kutsia, T. (eds) Algebraic Biology. AB 2007. Lecture Notes in Computer Science, vol 4545. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-73433-8_22
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DOI: https://doi.org/10.1007/978-3-540-73433-8_22
Publisher Name: Springer, Berlin, Heidelberg
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