Cyclic flats of binary matroids

Ragnar Freij-Hollanti; Matthias Grezet; Camilla Hollanti; Thomas Westerbäck

doi:10.1016/j.aam.2021.102165

Cyclic flats of binary matroids

Ragnar Freij-Hollanti^*, Matthias Grezet, Camilla Hollanti, Thomas Westerbäck

^*Tämän työn vastaava kirjoittaja

Matematiikan ja systeemianalyysin laitos

Tutkimustuotos: Lehtiartikkeli › Article › Scientific › vertaisarvioitu

1 Sitaatiot (Scopus)

54 Lataukset (Pure)

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In this paper, first steps are taken towards characterizing rank-decorated lattices of cyclic flats Z(M) that belong to matroids M that can be represented over a prescribed finite field F_q. Two natural maps from Z(M) to the lattice of cyclic flats of a minor of M are given. Binary matroids are characterized via their lattice of cyclic flats. It is shown that the lattice of cyclic flats of a simple binary matroid without isthmuses is atomic.

Alkuperäiskieli	Englanti
Artikkeli	102165
Sivumäärä	47
Julkaisu	Advances in Applied Mathematics
Vuosikerta	127
DOI - pysyväislinkit	https://doi.org/10.1016/j.aam.2021.102165
Tila	Julkaistu - kesäk. 2021
OKM-julkaisutyyppi	A1 Julkaistu artikkeli, soviteltu

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10.1016/j.aam.2021.102165Lisenssi: CC BY-NC-ND

Freij-Hollanti_Cyclic_Flats.1-s2.0-S0196885821000038-main-1Final published version, 597 KBLisenssi: CC BY-NC-ND

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Lukuteoreettisia ja kombinatorisia työkaluja yksityisiin ja turvallisiin pilvipalveluihin
Hollanti, C., Arabi Kakavandfaramani, M., Grezet, M., Damir, M., Tajeddine, R., Westerbäck, T. & Blomqvist, F.
01/07/2016 → 30/06/2018
Projekti: Academy of Finland: Other research funding
Sovellettu algebra ja lukuteoria kestävien ja turvallisten langattomien pilvitallennussysteemien suunnittelussa
Hollanti, C., Amoros Carafi, L., Tran Nguyen Thanh, H., Blanco Chacon, I., Keränen, J. & Vesalainen, E.
01/09/2014 → 31/08/2018
Projekti: Academy of Finland: Other research funding
Sovellettu algebra tietoliikenneteknologiassa
Hollanti, C., Gnilke, O., Greferath, M., Blomqvist, F. & Barreal Fernandez, A.
01/09/2014 → 31/08/2019
Projekti: Academy of Finland: Other research funding

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@article{dae6d27c78094f19ab47a23d55fdcd3f,

title = "Cyclic flats of binary matroids",

abstract = "In this paper, first steps are taken towards characterizing rank-decorated lattices of cyclic flats Z(M) that belong to matroids M that can be represented over a prescribed finite field Fq. Two natural maps from Z(M) to the lattice of cyclic flats of a minor of M are given. Binary matroids are characterized via their lattice of cyclic flats. It is shown that the lattice of cyclic flats of a simple binary matroid without isthmuses is atomic.",

keywords = "Atomic lattices, Binary matroids, Cyclic flats",

author = "Ragnar Freij-Hollanti and Matthias Grezet and Camilla Hollanti and Thomas Westerb{\"a}ck",

note = "Funding Information: The work of M. Grezet, C. Hollanti, and T. Westerb{\"a}ck was supported in part by The Academy of Finland [grant numbers 276031 , 282938 , and 303819 ] and by the Technical University of Munich – Institute for Advanced Study, funded by the German Excellence Initiative and the EU 7th Framework Programme [grant number 291763 ], via a Hans Fischer Fellowship. R. Freij-Hollanti was supported by the German Research Foundation ( Deutsche Forschungsgemeinschaft , DFG) [grant number WA3907/1-1 ]. Publisher Copyright: {\textcopyright} 2021 The Author(s) Copyright: Copyright 2021 Elsevier B.V., All rights reserved.",

year = "2021",

month = jun,

doi = "10.1016/j.aam.2021.102165",

language = "English",

volume = "127",

journal = "Advances in Applied Mathematics",

issn = "0196-8858",

publisher = "Academic Press",

}

TY - JOUR

T1 - Cyclic flats of binary matroids

AU - Freij-Hollanti, Ragnar

AU - Grezet, Matthias

AU - Hollanti, Camilla

AU - Westerbäck, Thomas

N1 - Funding Information: The work of M. Grezet, C. Hollanti, and T. Westerbäck was supported in part by The Academy of Finland [grant numbers 276031 , 282938 , and 303819 ] and by the Technical University of Munich – Institute for Advanced Study, funded by the German Excellence Initiative and the EU 7th Framework Programme [grant number 291763 ], via a Hans Fischer Fellowship. R. Freij-Hollanti was supported by the German Research Foundation ( Deutsche Forschungsgemeinschaft , DFG) [grant number WA3907/1-1 ]. Publisher Copyright: © 2021 The Author(s) Copyright: Copyright 2021 Elsevier B.V., All rights reserved.

PY - 2021/6

Y1 - 2021/6

N2 - In this paper, first steps are taken towards characterizing rank-decorated lattices of cyclic flats Z(M) that belong to matroids M that can be represented over a prescribed finite field Fq. Two natural maps from Z(M) to the lattice of cyclic flats of a minor of M are given. Binary matroids are characterized via their lattice of cyclic flats. It is shown that the lattice of cyclic flats of a simple binary matroid without isthmuses is atomic.

AB - In this paper, first steps are taken towards characterizing rank-decorated lattices of cyclic flats Z(M) that belong to matroids M that can be represented over a prescribed finite field Fq. Two natural maps from Z(M) to the lattice of cyclic flats of a minor of M are given. Binary matroids are characterized via their lattice of cyclic flats. It is shown that the lattice of cyclic flats of a simple binary matroid without isthmuses is atomic.

KW - Atomic lattices

KW - Binary matroids

KW - Cyclic flats

UR - http://www.scopus.com/inward/record.url?scp=85100033597&partnerID=8YFLogxK

U2 - 10.1016/j.aam.2021.102165

DO - 10.1016/j.aam.2021.102165

M3 - Article

AN - SCOPUS:85100033597

VL - 127

JO - Advances in Applied Mathematics

JF - Advances in Applied Mathematics

SN - 0196-8858

M1 - 102165

ER -

Cyclic flats of binary matroids

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Lukuteoreettisia ja kombinatorisia työkaluja yksityisiin ja turvallisiin pilvipalveluihin

Sovellettu algebra ja lukuteoria kestävien ja turvallisten langattomien pilvitallennussysteemien suunnittelussa

Sovellettu algebra tietoliikenneteknologiassa

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