Phylogenetic invariants for ${\mathbb{Z}}_3$ scheme-theoretically

Abstract

We study phylogenetic invariants of models of evolution whose group of symmetries is the cyclic group with 3 elements. We prove that projective schemes corresponding to the ideal I of phylogenetic invariants of such a model and to its subideal I' generated by elements of degree at most 3 are the same. This is motivated by a conjecture of Sturmfels and Sullivant, which would imply that I = I'.

17 pages; v2: exposition significantly improved

References in corpus (2)

• On the toric ideal of a matroid
• Constructive degree bounds for group-based models