  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.
