Growth rate functions of dense classes of representable matroids
arXiv:1105.4162
Abstract
For each proper minor-closed subclass $\cM$ of the $\GF(q^2)$-representable matroids containing all simple $\GF(q)$-representable matroids, we give, for all large , a tight upper bound on the number of points in a rank- matroid in $\cM$, and construct a rank- matroid in $\cM$ for which equality holds. As a consequence, we give a tight upper bound on the number of points in a $\GF(q^2)$-representable, rank- matroid with no $\PG(k,q^2)$-minor.