For any fair division instance with monotone valuations, there exists an allocation with copies where each agent gets at least its maximin share, no good is copied more than O(log m) times, and total copies are at most m.
Fair division under cardinality constraints
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Exact Maximin Share Fairness via Adjusted Supply
For any fair division instance with monotone valuations, there exists an allocation with copies where each agent gets at least its maximin share, no good is copied more than O(log m) times, and total copies are at most m.