Finite phylogenetic complexity and combinatorics of tables

TL;DR

This paper proves that the phylogenetic complexity, an invariant related to algebraic statistics and phylogenetics, is finite for all finite abelian groups, advancing understanding in algebraic combinatorics.

Contribution

It establishes the finiteness of the phylogenetic complexity for all finite abelian groups, a previously unresolved question.

Findings

Phylogenetic complexity is finite for all finite abelian groups.

Provides new insights into the combinatorics of tables in algebraic statistics.

Advances the theoretical understanding of invariants in phylogenetics.

Abstract

We prove that the phylogenetic complexity -- an invariant introduced by Sturmfels and Sullivant -- of any finite abelian group is finite.