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

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