A celebrated analogy between prime factorizations of integers and cycle decompositions of permutations is explored here. Asymptotic formulas characterizing semismooth numbers (possessing at most several large factors) carry over to random permutations. We offer a survey of practical methods for computing relevant probabilities of a bivariate or trivariate flavor.

翻译：此处探讨了整数和周期分解的原始系数之间的一个值得称道的类比。 以半单位数( 最多包含数大因素) 为特征的零食式公式会传到随机变异中。 我们提供了计算双轨或三轨口味相关概率的实用方法调查 。