Matroids Arising From Nested Sequences of Flats In Projective And Affine Geometries

TL;DR

This paper characterizes forbidden induced restrictions for matroids derived from nested sequences of flats in projective and affine geometries over finite fields, generalizing previous binary results.

Contribution

It extends the classification of matroids from binary to general finite fields and identifies forbidden restrictions for affine and projective geometry-based matroids.

Findings

Forbidden induced restrictions for projective geometry targets over GF(q)

Forbidden restrictions for affine geometry targets

Generalization of binary case to finite fields

Abstract

Targets are matroids that arise from a nested sequence of flats in a projective geometry. This class of matroids was introduced by Nelson and Nomoto, who found the forbidden induced restrictions for binary targets. This paper generalizes their result to targets arising from projective geometries over $GF(q)$. We also consider targets arising from nested sequences of affine flats and determine the forbidden induced restrictions for affine targets.