Sequential selection of a monotone subsequence from a random permutation

Peng, Peichao; Steele, J.

doi:10.1090/proc/13104

Sequential selection of a monotone subsequence from a random permutation
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by Peichao Peng and J. Michael Steele PDF

Proc. Amer. Math. Soc. 144 (2016), 4973-4982 Request permission

Abstract:

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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