Finite phylogenetic complexity and combinatorics of tables

Michałek, Mateusz; Ventura, Emanuele

doi:10.2140/ant.2017.11.235

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Finite phylogenetic complexity and combinatorics of tables

Mateusz Michałek and Emanuele Ventura

Vol. 11 (2017), No. 1, 235–252

DOI: 10.2140/ant.2017.11.235

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 $X (G, K_{1, n})$ . 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 $X (G, K_{1, n})$ are generated in degree at most $ϕ$ .

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

Vol. 11, No. 1, 2017