Finite phylogenetic complexity of Z(p) and invariants for Z(3)

Mateusz Michalek

doi:10.1016/j.ejc.2016.08.007

Finite phylogenetic complexity of Z(p) and invariants for Z(3)

Mateusz Michalek^*

^*Corresponding author for this work

Not published at Aalto University

Polish Academy of Sciences

Research output: Contribution to journal › Article › Scientific › peer-review

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 Petrovic, 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. (C) 2016 Elsevier Ltd. All rights reserved.

Original language	English
Pages (from-to)	169-186
Number of pages	18
Journal	European Journal of Combinatorics
Volume	59
DOIs	https://doi.org/10.1016/j.ejc.2016.08.007
Publication status	Published - Jan 2017
MoE publication type	A1 Journal article-refereed

Keywords

TORIC FIBER PRODUCTS
GROUP-BASED MODELS
COMBINATORIAL NULLSTELLENSATZ
GEOMETRY

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10.1016/j.ejc.2016.08.007

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title = "Finite phylogenetic complexity of Z(p) and invariants for Z(3)",

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 Petrovic, 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. (C) 2016 Elsevier Ltd. All rights reserved.",

keywords = "TORIC FIBER PRODUCTS, GROUP-BASED MODELS, COMBINATORIAL NULLSTELLENSATZ, GEOMETRY",

author = "Mateusz Michalek",

year = "2017",

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doi = "10.1016/j.ejc.2016.08.007",

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T1 - Finite phylogenetic complexity of Z(p) and invariants for Z(3)

AU - Michalek, Mateusz

PY - 2017/1

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N2 - 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 Petrovic, 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. (C) 2016 Elsevier Ltd. All rights reserved.

AB - 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 Petrovic, 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. (C) 2016 Elsevier Ltd. All rights reserved.

KW - TORIC FIBER PRODUCTS

KW - GROUP-BASED MODELS

KW - COMBINATORIAL NULLSTELLENSATZ

KW - GEOMETRY

U2 - 10.1016/j.ejc.2016.08.007

DO - 10.1016/j.ejc.2016.08.007

M3 - Article

SN - 0195-6698

VL - 59

SP - 169

EP - 186

JO - European Journal of Combinatorics

JF - European Journal of Combinatorics

ER -

Finite phylogenetic complexity of Z(p) and invariants for Z(3)

Abstract

Keywords

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