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

^*Corresponding author for this work

Mälardalen University

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

5 Citations (Scopus)

142 Downloads (Pure)

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 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.

Original language	English
Article number	102165
Number of pages	47
Journal	Advances in Applied Mathematics
Volume	127
DOIs	https://doi.org/10.1016/j.aam.2021.102165
Publication status	Published - Jun 2021
MoE publication type	A1 Journal article-refereed

Keywords

Atomic lattices
Binary matroids
Cyclic flats

Access to Document

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

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

Cite this

@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

SN - 0196-8858

VL - 127

JO - Advances in Applied Mathematics

JF - Advances in Applied Mathematics

M1 - 102165

ER -

Cyclic flats of binary matroids

Abstract

Keywords

Access to Document

Other files and links

Number-theoretic and combinatorial tools for private and secure cloud services

Applied Algebra and Number Theory in Robust and Secure Wireless Cloud Storage Systems

Applied algebra in communications technology

Cite this

Cyclic flats of binary matroids

Abstract

Keywords

Access to Document

Other files and links

Projects

Number-theoretic and combinatorial tools for private and secure cloud services

Applied Algebra and Number Theory in Robust and Secure Wireless Cloud Storage Systems

Applied algebra in communications technology

Cite this