Growth rate functions of dense classes of representable matroids

Details Growth rate functions of dense classes of representable matroids Growth rate functions of dense classes of representable matroids

2011-05-20

arxiv.org/abs/1105.4162v1

Mathematics

Combinatorics

Scientific paper

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 $r$, a tight upper bound on the number of points in a rank-$r$ matroid in $\cM$, and construct a rank-$r$ 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-$r$ matroid with no $\PG(k,q^2)$-minor.

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