At most $3.55^n$ stable matchings

Abstract

We improve the upper bound for the maximum possible number of stable matchings among $n$ jobs and $n$ applicants from $131072^n+O(1)$ to $3.55^n+O(1)$. To establish this bound, we state a novel formulation of a certain entropy bound that is easy to apply and may be of independent interest in counting other combinatorial objects