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Prime numbers, diophantine equations, diophantine approximations, analytic or algebraic number theory, arithmetic geometry, Galois theory, transcendental number theory, continued fractions

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Analogy between Integers and Permutations

The essential common feature that insures convergence to a Poisson Dirichlet distribution is explained in the book "Logarithmic Combinatorial Structures" by Arratia Barbour and Tavare. They do a great …
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Analogy between Integers and Permutations

If I remember well, there is also a correspondence between the degrees of factors of polynomials in $\mathbb{F}_q[X]$, the size of cycles of riffle-shuffle permutations (a brand of non-uniform random …
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