On pancyclic representable matroids

Bondy proved that an n-vertex simple Hamiltonian graph with at least n2/4 edges has cycles of every length unless it is isomorphic to Kn/2,n/2. This paper considers finding circuits of every size in GF (q)-representable matroids with large numbers of elements. A consequence of the main result is that a rank-r simple binary matroid with at least 2r−1 elements has circuits of all sizes or is isomorphic to AG(r − 1, 2) or PG(r − 2, 2)⊕ U1,1.