The long-line graph of a combinatorial geometry. II. Geometries representable over two fields of different characteristics

AbstractLet q be a power of a prime and let s be zero or a prime not dividing q. Then the number of points in a combinatorial geometry (or simple matroid) of rank n which is representable over GF(q) and a field of characteristic s is at most (qν − qν−1)(2n+1)−n, where ν = 2q−1 − 1