  Let $\cX$ be a family of subsets of a finite set $E$. A matroid on $E$ is
called an $\cX$-matroid if each set in $\cX$ is a circuit. We consider the
problem of determining when there exists a unique maximal $\cX$-matroid in the
weak order poset of all $\cX$-matroids on $E$, and characterizing its rank
function when it exists.
