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Consider a sequence X_1, X_2,... of i.i.d. uniform random variables takingvalues in the alphabet set {1,2,...,d}. A k-superpattern is a realization ofX_1,...,X_t that contains, as an embedded subsequence, each of thenon-order-isomorphic subpatterns of length k. We focus on the non-trivial caseof d=k=3 and study the waiting time distribution of tau=inf{t>=7: X_1,...,X_tis a superpattern}

Waiting Time Distribution for the Emergence of Superpatterns