Finite phylogenetic complexity of Zp and invariants for Z3. (January 2017) - Michałek, Mateusz
Abstract: We study phylogenetic complexity of finite abelian groups—an invariant introduced by Sturmfels and Sullivant (2005). The invariant is hard to compute—so far it was only known for Z 2, in which case it equals 2 (Sturmfels and Sullivant, 2005), (Chifman and Petrović, 2007). We prove that phylogenetic complexity of any group Z p, where p is prime, is finite. We also show, as conjectured by Sturmfels and Sullivant, that the phylogenetic complexity of Z 3 equals 3 .