Dense PG(n-1,2)-free binary matroids

Abstract

For each integer $n\ge 2$, we prove that, if $M$ is a simple rank-$r$ $PG(n-1,2)$-free binary matroid with $|M|>\left(1-\frac{3}{2^n}\right)2^r$, then there is a triangle-free corank-$(n-2)$ flat of $M$.

arXiv comment11 pages. Submitted for publication in JCTb

References in corpus (2)

• Dense binary $PG(t-1,2)$-free matroids have critical number $t-1$ or $t$
• The critical number of dense triangle-free binary matroids