Packing and covering with matroid circuits

AbstractWe prove a conjecture of Welsh, that for every matroid M without coloops, ν(M) + θ(M) ≤ ϱ(M) + κ(M) where ν(M) is the maximum number of pairwise disjoint circuits, θ(M) is the minimum number of circuits whose union is E(M), ϱ(M) is the corank of M, and κ(M) is the number of connected components of M. For binary matroids the result was previously proved by Oxley