Every finite distributive lattice is a set of stable matchings
Each of 2n people, n men and n women, has a linear preference ordering on those of the opposite sex. A matching, i.e. forming n couples, is called stable if one cannot find a woman in one couple and a man in another who would prefer each other to their present partners. The set of stable matchings forms a distributive lattice by defining a partial ordering as follows: one matching is \(\geq\) another if every man is at least as happy with his partner in the first matching as in the second. In this note the author shows that each finite distributive lattice can be represented by a set of stable matchings.
scientific article; zbMATH DE number 3869398