The formal introduction is in the text. For reference, the particular example that we considered was with preferences as follows.
Companies (ranking of applicants) ---------- Google: W,X,Z,Y NSA: W,Y,Z,X Boeing: X,W,Y,Z Microsoft: W,Z,X,Y Applicants (ranking of companies) ---------- W: Microsoft,NSA,Boeing,Google X: Microsoft,NSA,Google,Boeing Y: Google,Microsoft,NSA,Boeing Z: NSA,Google,Microsoft,Boeing
The stable marriage solution that we identifed, was as follows:
(Google,X) (NSA,Y) (Boeing,Z) (Microsoft,W)Though we have not proved so, in this particuar instance, this is the only legal solution (more generally, there may be many).