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
翻译:我们改进了最低稳定匹配数量上限的上限,以尽可能在10美元和申请人之间实现最大数量的稳定匹配,从131072美元+O(1)美元提高到355美元+O(1)美元。为了确定这一上限,我们陈述了一种新颖的、易于应用的、在计算其他组合对象方面可能具有独立利益的某种加密约束的配方。