A flat of a matroid is cyclic if it is a union of circuits. The cyclic flats
of a matroid form a lattice under inclusion. We study these lattices and
explore matroids from the perspective of cyclic flats. In particular, we show
that every lattice is isomorphic to the lattice of cyclic flats of a matroid.
We give a necessary and sufficient condition for a lattice Z of sets and a
function r on Z to be the lattice of cyclic flats of a matroid and the
restriction of the corresponding rank function to Z. We define cyclic width and
show that this concept gives rise to minor-closed, dual-closed classes of
matroids, two of which contain only transversal matroids.Comment: 15 pages, 1 figure. The new version addresses earlier work by Julie
Sims that the authors learned of after submitting the first versio