Clonal sets in GF(q)GF(q)-representable matroids

Whittle [12] conjectured that if MM is a 33-connected quaternary matroid with a clonal pair {e,f}{e,f}, then M∖e,fM∖e,f and M/e,fM/e,f are both binary. In this paper we show that for q∈{4,5,7,8,9}q∈{4,5,7,8,9} if MM is a 3-connected GF(q)GF(q)-representable matroid with a clonal set XX of size q−2q−2, then M∖XM∖X and M/XM/X are binary.