Finite phylogenetic complexity of Zp and invariants for Z3. (January 2017)

• Record Type: Journal Article
• Authors: Michałek, Mateusz
• Is Part Of: European journal of combinatorics. Volume 59(2017)
• Page Start: 169
• Page End: 186
• Publication Date: 2017-01
• Subjects: Combinatorial analysis -- Periodicals; Analyse combinatoire -- Périodiques; Combinatorial analysis; Periodicals; Electronic journals; 511.6
• DOI: 10.1016/j.ejc.2016.08.007
• Languages: English
• ISSNs: 0195-6698

Abstract

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 .