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)

127 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

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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

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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",

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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

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U2 - 10.1016/j.aam.2021.102165

DO - 10.1016/j.aam.2021.102165

M3 - Article

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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

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

Applied algebra in communications technology

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

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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 in communications technology

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

Cite this