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سند علمی

Toric Ideals of Phylogenetic Invariants for the General Group-Based Model on Claw Trees K 1, n

Julia Chifman, Sonja Petrovic

چکیده

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. Acknowledgment. The authors would like to thank Uwe Nagel for introducing us to the field of phylogenetic algebraic geometry and for his continuous support, motivation and guidance.

اسناد مشابه

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