  We study fair and economically efficient allocation of indivisible goods
among agents whose valuations are rank functions of matroids. Such valuations
constitute a well-studied class of submodular functions (i.e., they exhibit a
diminishing returns property) and model preferences in several
resource-allocation settings. We prove that, for matroid-rank valuations, a
social welfare-maximizing allocation that gives each agent her maximin share
always exists. Furthermore, such an allocation can be computed in polynomial
time. We establish similar existential and algorithmic results for the pairwise
maximin share guarantee as well.
  To complement these results, we show that if the agents have binary XOS
valuations or weighted-rank valuations, then maximin fair allocations are not
guaranteed to exist. Both of these valuation classes are immediate
generalizations of matroid-rank functions.
