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Unavoidable flats in matroids excluding a uniform minor
Abstract
We extend a theorem of Geelen, Kroeker, and Nelson on unavoidable flats in GF(q)-representable matroids. For all integers 1≤ a≤ b and n≥1, we prove that every simple matroid of sufficiently large rank with no Ua,b-minor has a rank-n flat whose restriction is free or isomorphic to a projective or affine geometry over a finite field.
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BibTeX
@misc{ge2026unavoidable,
title = {{Unavoidable flats in matroids excluding a uniform minor}},
author = {Wayne Ge},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.41096},
eprint = {2610.41096},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.41096},
}
RIS
TY - UNPB
TI - Unavoidable flats in matroids excluding a uniform minor
AU - Wayne Ge
PY - 2026
DA - 2026/10/30
PB - arXiv
DO - 10.48550/arxiv.2610.41096
UR - https://arxiv.org/abs/2610.41096
AB - We extend a theorem of Geelen, Kroeker, and Nelson on unavoidable flats in GF(q)-representable matroids. For all integers 1≤ a≤ b and n≥1, we prove that every simple matroid of sufficiently large rank with no U_a,b-minor has a rank-n flat whose restriction is free or isomorphic to a projective or affine geometry over a finite field.
ER -