The Set of Stable Matchings and the Core in a Matching Market with Ties and Matroid Constraints

In this paper, we consider a many-to-one matching market where ties in the preferences of agents are allowed. For this market with capacity constraints, Bonifacio, Juarez, Neme, and Oviedo proved some relationship between the set of stable matchings and the core. In this paper, we consider a matroid constraint that is a generalization of a capacity constraint. We prove that the results proved by Bonifacio, Juarez, Neme, and Oviedo can be generalized to this setting.