We unify Ryser's and Glynn's formulas for computing the permanent into a single framework. We then show via an orbital bound argument that the product rank of the permanent is asymptotically upper bounded by $ \frac{\exp\left(\pi\sqrt{\frac{2n}{3}}\right)}{4\sqrt{3}n} $.

翻译：我们统一了Ryser和Glynn用于计算积和式的公式，将其整合至单一框架中。随后通过轨道界论证表明，积和式的乘积秩渐近上界为$ \frac{\exp\left(\pi\sqrt{\frac{2n}{3}}\right)}{4\sqrt{3}n} $。