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

Department of Mathematics and Systems Analysis

Mälardalen University

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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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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.",

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

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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.

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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.

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KW - Cyclic flats

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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

OpenUrl availability

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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

Cite this