  The scale invariant Poisson processes on (0,infty) play a central but mildly
disguised role in number theory, combinatorics, and genetics. They give the
continuous limits which underly and unify diverse discrete structures,
including the prime factorization of a uniformly chosen integer, the
factorization of polynomials over finite fields, the decomposition into cycles
of random permutations, the decomposition into components of random mappings,
and the Ewens sampling formula. They deserve attention as one of the
fundamental and central objects of probability theory.
