Abstract :
The function, f(n), represents the maximum number of stable matchings possible in an instance of size n of the stable marriage problem. It is shown that f(n) is a strictly increasing function of n, and a result of Knuthʹs concerning the exponential growth of this function is generalized to apply to all positive integers, n. A method for constructing ranking matrices is used to produce instances with many stable matchings. A subproblem of the stable marriage problem developed by Eilers (Irvine Compiler Corporation Technical Report, ICC TR1999-2, 1999), called the pseudo-Latin marriage problem, plays a significant role as a tool and as motivation in the paper.
