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For a many-to-many matching market, we study the lattice structure of the setof random stable matchings. We define a partial order on the random stable setand present two intuitive binary operations to compute the least upper boundand the greatest lower bound for each side of the matching market. Then, weprove that with these binary operations the set of random stable matchingsforms two dual lattices.

Lattice structure of the random stable set in many-to-many matching market