Cyclic flats of binary matroids

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

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Cyclic flats of binary matroids

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Title:	Cyclic flats of binary matroids
Author(s):	Freij-Hollanti, Ragnar ; Grezet, Matthias ; Hollanti, Camilla ; Westerbäck, Thomas
Date:	2021-06
Language:	en
Pages:	47
Department:	Department of Mathematics and Systems Analysis Mälardalen University
Series:	Advances in Applied Mathematics, Volume 127
ISSN:	0196-8858
DOI-number:	10.1016/j.aam.2021.102165
Keywords:	Atomic lattices, Binary matroids, Cyclic flats
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Citation: Freij-Hollanti , R , Grezet , M , Hollanti , C & Westerbäck , T 2021 , ' Cyclic flats of binary matroids ' , Advances in Applied Mathematics , vol. 127 , 102165 . https://doi.org/10.1016/j.aam.2021.102165
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.

Description: 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.
Permanent link to this item: http://urn.fi/URN:NBN:fi:aalto-202105196832 Email this Export to RefWorks QR Code Print BibTex Tweet