#### Vol. 11, No. 1, 2017

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Finite phylogenetic complexity and combinatorics of tables

### Mateusz Michałek and Emanuele Ventura

Vol. 11 (2017), No. 1, 235–252
##### Abstract

In algebraic statistics, Jukes–Cantor and Kimura models are of great importance. Sturmfels and Sullivant generalized these models by associating to any finite abelian group $G$ a family of toric varieties $X\left(G,{K}_{1,n}\right)$. We investigate the generators of their ideals. We show that for any finite abelian group $G$ there exists a constant $\varphi$, depending only on $G$, such that the ideals of $X\left(G,{K}_{1,n}\right)$ are generated in degree at most $\varphi$.

##### Keywords
Phylogenetics, Toric varieties, Convex polytopes, Applied Algebraic Geometry
##### Mathematical Subject Classification 2010
Primary: 52B20
Secondary: 14M25, 13P25