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Dirichlet law for factorisation of integers, polynomials and permutations
Published online by Cambridge University Press: 06 September 2023
Abstract
Let $k \geqslant 2$ be an integer. We prove that factorisation of integers into k parts follows the Dirichlet distribution $\mathrm{Dir}\left({1}/{k},\ldots,{1}/{k}\right)$ by multidimensional contour integration, thereby generalising the Deshouillers–Dress–Tenenbaum (DDT) arcsine law on divisors where $k=2$. The same holds for factorisation of polynomials or permutations. Dirichlet distribution with arbitrary parameters can be modelled similarly.
- Type
- Research Article
- Information
- Mathematical Proceedings of the Cambridge Philosophical Society , Volume 175 , Issue 3 , November 2023 , pp. 649 - 676
- Copyright
- © The Author(s), 2023. Published by Cambridge University Press on behalf of Cambridge Philosophical Society