The number of points in a matroid with no n-point line as a minor

Details The number of points in a matroid with no n-point line as a minor The number of points in a matroid with no n-point line as a minor

2011-05-20

arxiv.org/abs/1105.4163v1

J. Combin. Theory. Ser. B 100 (2010), 625-630

Mathematics

Combinatorics

Scientific paper

For any positive integer $l$ we prove that if $M$ is a simple matroid with no
$(l+2)$-point line as a minor and with sufficiently large rank, then $|E(M)|\le
\frac{q^{r(M)}-1}{q-1}$, where $q$ is the largest prime power less than or
equal to $l$. Equality is attained by projective geometries over GF$(q)$.

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