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Choose a random polynomial f uniformly from among the q d (q − 1) polynomials of degree d in F q [x]. Let c k be the number of cycles of length k in the directed graph on F q with edges {(v, f (v))} v∈Fq. If d = d(q) → ∞ as q → ∞, then the numbers c 1 , c 2 ,. .. , c b are asymptotically independent Poisson(1/k), just as in the classical theory of random… (More)

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