论文标题
DIRICHLET定律，用于分解整数，多项式和排列
Dirichlet law for factorization of integers, polynomials and permutations
论文作者
论文摘要
令$ k \ geq 2 $为整数。 We prove that factorization of integers into $k$ parts follows the Dirichlet distribution $\text{Dir}\left(\frac{1}{k},\ldots,\frac{1}{k}\right)$ by multidimensional contour integration, thereby generalizing the Deshouillers-Dress-Tenenbaum (DDT) arcsine law on divisors where $ k = 2 $。对于多项式或排列的分解也有相同的成分。具有任意参数的Dirichlet分布可以类似地建模。
Let $k \geq 2$ be an integer. We prove that factorization of integers into $k$ parts follows the Dirichlet distribution $\text{Dir}\left(\frac{1}{k},\ldots,\frac{1}{k}\right)$ by multidimensional contour integration, thereby generalizing the Deshouillers-Dress-Tenenbaum (DDT) arcsine law on divisors where $k=2$. The same holds for factorization of polynomials or permutations. Dirichlet distribution with arbitrary parameters can be modelled similarly.
