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Let the random variable Z n,k denote the number of increasing subse-quences of length k in a random permutation from

Consider a permutation σ ∈ S n as a deck of cards numbered from 1 to n and laid out in a row, where σ j denotes the number of the card that is in the j-th position from the left. We study some probabilistic and combina-torial aspects of the shuffle on S n defined by removing and then randomly reinserting each of the n cards once, with the removal and… (More)

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