Cliques in dense GF(\(q\))-representable matroids (Q1405118)

The authors prove the following conjecture of \textit{J. P. S. Kung} [Contemp. Math. 147, 21-61 (1993; Zbl 0791.05018)]: For any field \(F\) and clique \(K_n\) there exists an integer \(\lambda\) such that, if \(M\) is a simple \(F\)-representable matroid with no \(M(K_n)\)-minor, then \(|E(M)|\leq\lambda r(M)\).