Cyclic flats of binary matroids

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

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

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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 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.

Original languageEnglish
Article number102165
Number of pages47
JournalAdvances in Applied Mathematics
Volume127
DOIs
Publication statusPublished - Jun 2021
MoE publication typeA1 Journal article-refereed

Keywords

  • Atomic lattices
  • Binary matroids
  • Cyclic flats

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