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

Rutger Campbell

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 co…