John D. Cook • 6/4/2026

Partitions over permutations

This article examines the double exponential function exp(exp(y)) and its power series coefficients, which involve Bell numbers (counting set partitions) and factorials (counting permutations). It provides Python code using SymPy to compute the ratio of partitions to permutations for labeled sets, discusses asymptotic approximations using logarithms and the Lambert W function, and notes the slow convergence of the series. The content is mathematically focused on combinatorics and functions, relevant to computer science and mathematical computing.

0 comments

#permutations #Partitions #Asymptotics