Quasirandom permutations are characterized by 4-point densities
Abstract
For permutations P and T of lengths |P||T|, let t(P,T) be the probability that the restriction of T to a random |P|-point set is (order) isomorphic to P. We show that every sequence \Tj\ of permutations such that |Tj|∞ and t(P,Tj) 1/4! for every 4-point permutation P is quasirandom (that is, t(P,Tj) 1/|P|! for every P). This answers a question posed by Graham.
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