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^*

^*Tämän työn vastaava kirjoittaja

Ei julkaistu Aalto-yliopiston affiliaatiolla

Polish Academy of Sciences

Tutkimustuotos: Lehtiartikkeli › Article › Scientific › vertaisarvioitu

1 Viittaus (Web of Science)

Abstrakti

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.

Alkuperäiskieli	Englanti
Sivut	169-186
Sivumäärä	18
Julkaisu	European Journal of Combinatorics
Vuosikerta	59
DOI - pysyväislinkit	https://doi.org/10.1016/j.ejc.2016.08.007
Tila	Julkaistu - tammik. 2017
OKM-julkaisutyyppi	A1 Alkuperäisartikkeli tieteellisessä aikakauslehdessä

Rahoitus

Supported by a grant Iuventus Plus of the Polish Ministry of Science project 0301/IP3/2015/73.

Pääsy asiakirjaan

10.1016/j.ejc.2016.08.007

Siteeraa tätä

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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",

month = jan,

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

language = "English",

volume = "59",

pages = "169--186",

journal = "European Journal of Combinatorics",

issn = "0195-6698",

publisher = "Elsevier",

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TY - JOUR

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

AU - Michalek, Mateusz

PY - 2017/1

Y1 - 2017/1

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)

Abstrakti

Rahoitus

Pääsy asiakirjaan

Sormenjälki

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