Constructing prime-field planar configurations
Gary Gordon · Proceedings of the American Mathematical Society · 1984
An infinite class of planar configurations is constructed with distinct prime-field characteristic sets (i.e., configurations represented over a finite set of prime fields but over fields of no other characteristic). It is shown that if p p is sufficiently large, then every subset of k k primes between p p and f ( p , k ) f(p,k) forms such a set (where f ( p , k ) = 2 [ ( p − A k 3 / 2 ) / B k 3 / 2 ] f(p,k) = {2^{[(\sqrt p - A{k^{3/2}})/B{k^{3/2}}]}} for constants A A and B B ). In particular, for every positive integer k k , there exist infinitely many planar matroid configurations C i , k {C_{i,k}} with | χ p f