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(G,K1,n). We investigate the generators of their ideals. We show that for any finite abelian group G there exists a constant ϕ, depending only on G, such that the ideals of X(G,K1,n) are generated in degree at most ϕ.

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Keywords
Phylogenetics, Toric varieties, Convex polytopes, Applied Algebraic Geometry
Mathematical Subject Classification 2010
Primary: 52B20
Secondary: 14M25, 13P25
Milestones
Received: 23 June 2016
Revised: 1 October 2016
Accepted: 12 November 2016
Published: 23 January 2017
Authors
Mateusz Michałek
Polish Academy of Sciences
Warsaw
Poland
Emanuele Ventura
Department of Mathematics and Systems Analysis
Aalto University
FI-00076 Espoo
Finland