The Number of Stable Matchings in Models of the Gale–shapley Type with Preferences given by Partial Orders

From the famous Gale–Shapley theorem we know that each classical marriage problem admits at least one stable matching. This fact has inspired researchers to search for the maximum number of possible stable matchings, which is equivalent to finding the minimum number of unstable matchings among all such problems of size n. In this paper, we deal with this issue for the Gale–Shapley model with preferences represented by arbitrary partial orders. Also, we discuss this model in the context of the classical Gale–Shapley model.