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The Lattice of Core (Sub)Matchings in a Two-Sided Matching Market
Thomas Quint
Source abstract
We consider the two-sided matching model of Demange and Gale (1985). Given a suitable partial ordering and a correct definition of “matching,” we show the set of core matchings is (under a nondegeneracy assumption) always a lattice. The results parallel the “set of core matchings is a lattice” theorem (Conway, in Knuth 1976) for the marriage market of Gale and Shapley (1962).
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