  We consider the problem of fairly allocating indivisible goods, among agents,
under cardinality constraints and additive valuations. In this setting, we are
given a partition of the entire set of goods---i.e., the goods are
categorized---and a limit is specified on the number of goods that can be
allocated from each category to any agent. The objective here is to find a fair
allocation in which the subset of goods assigned to any agent satisfies the
given cardinality constraints. This problem naturally captures a number of
resource-allocation applications, and is a generalization of the well-studied
(unconstrained) fair division problem.
  The two central notions of fairness, in the context of fair division of
indivisible goods, are envy freeness up to one good (EF1) and the (approximate)
maximin share guarantee (MMS). We show that the existence and algorithmic
guarantees established for these solution concepts in the unconstrained setting
can essentially be achieved under cardinality constraints. Specifically, we
develop efficient algorithms which compute EF1 and approximately MMS
allocations in the constrained setting.
  Furthermore, focusing on the case wherein all the agents have the same
additive valuation, we establish that EF1 allocations exist and can be computed
efficiently even under laminar matroid constraints.
