Sequential Selection of a Monotone Subsequence from a Random Permutation

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Business
Mathematics
Statistics and Probability
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Peng, Peichao
Steele, J. Michael
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We find a two term asymptotic expansion for the optimal expected value of a sequentially selected monotone subsequence from a random permutation of length n. A striking feature of this expansion is that it tells us that the expected value of optimal selection from a random permutation is quantifiably larger than optimal sequential selection from an independent sequence of uniformly distributed random variables; specifically, it is larger by at least (1/6) log n + O(1).

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2016-04-20
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