Clonal sets in -representable matroids

Whittle [12] conjectured that if M is a 3 -connected quaternary matroid with a clonal pair { e , f } , then M ∖ e , f and M / e , f are both binary. In this paper we show that for q ∈ { 4 , 5 , 7 , 8 , 9 } if M is a 3-connected G F ( q ) -representable matroid with a clonal set X of size q − 2 , then M ∖ X and M / X are binary.