What is the maximum number of stable marriages for an instance of the Stable Marriage Problem?
For an instance with $n$ men and $n$ women, the trivial upper bound is $n!$, and nothing better is known. For a lower bound, Knuth (1976) gives an infinite family of instances with $\Omega(2.28^n)$ stable matchings, and Thurber (2002) extends this family to all $n$.