Finite phylogenetic complexity ofZpand invariants forZ3

Abstract

Abstract. We study phylogenetic complexity of finite abelian groups -an invariant introduced by Sturmfels and Sullivant [SS05]. The invariant is hard to compute -so far it was only known for Z 2 , in which case it equals 2 [SS05, CP07]. 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.

Selected topics on toric varieties

“…Example 11.4 ( [Mic17]). For G = (Z 2 , +) and n = 6 consider the following two compatible tables: Note that the red subtable of T 0 is compatible with the table T ′ = 0 1 0 1 0 0 1 0 1 0 1 1 .…”