Cyclic Flats of Binary Matroids

2019/06/26 by Freij-Hollanti, Ragnar, Grezet, Matthias, Hollanti, Camilla +1
#Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.1906.10936

Abstract

In this paper, first steps are taken towards characterising lattices of cyclic flats Z(M) that belong to matroids M that can be represented over a prescribed finite field \mathbbF_q. Two natural maps from Z(M) to the lattice of cyclic flats of a minor of M are given. Binary matroids are characterised 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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