Cyclic flats of binary matroids

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Journal Title
Journal ISSN
Volume Title
A1 Alkuperäisartikkeli tieteellisessä aikakauslehdessä
Date
2021-06
Major/Subject
Mcode
Degree programme
Language
en
Pages
47
Series
Advances in Applied Mathematics, Volume 127
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.
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