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Creators/Authors contains: "Yoshikawa, Lino"

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  1. ; ; ; ; ; ; ; ; (, Pure Mathematics and Applications)
    Abstract Let π n be a uniformly chosen random permutation on [ n ]. Using an analysis of the probability that two overlapping consecutive k -permutations are order isomorphic, we show that the expected number of distinct consecutive patterns of all lengths k ∈ {1, 2,…, n } in π n is n 2 2 ( 1 - o ( 1 ) ) {{{n^2}} \over 2}\left( {1 - o\left( 1 \right)} \right) as n → ∞. This exhibits the fact that random permutations pack consecutive patterns near-perfectly. 
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