stable matching

A matching is a mapping from the elements of one set to the elements of the other set.
A matching is stable whenever it is not the case that both:
a.some given element A of the first matched set prefers some given element B of the
second matched set over the element to which A is already matched, and
b. B also prefers A over the element to which B is already matched

The matching in this case is according to men's preferences, to change it according
to women's preferences some trivial changes need to be made.