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For permutations \({\pi}\) and \({\tau}\) of lengths \({|\pi|\le|\tau|}\) , let \({t(\pi,\tau)}\) be the probability that the restriction of \({\tau}\) to a random \({|\pi|}\) -point set is (order) isomorphic to \({\pi}\) . We show that every sequence \({\{\tau_j\}}\) of permutations such that \({|\tau_j|\to\infty}\) and \({t(\pi,\tau_j)\to 1/4!}\) for every 4-point permutation \({\pi}\) is quasirandom (that is, \({t(\pi,\tau_j)\to 1/|\pi|!}\) for every \({\pi}\)). This answers a question posed by Graham.

Quasirandom permutations are characterized by 4-point densities