Dirichlet law for factorization of integers, polynomials and permutations

2022/06/29 by Leung, Sun-Kai
#Combinatorics (math.CO) #FOS: Mathematics #Number Theory (math.NT) #Probability (math.PR)

paper · doi:10.48550/arxiv.2206.14728

Abstract

Let k ≥ 2 be an integer. We prove that factorization of integers into k parts follows the Dirichlet distribution Dir((1)/(k),…,(1)/(k)) 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.

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