Date of this Version
Proceedings of the American Mathematical Society
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).
First published in Proc. Amer. Math. Soc. 144 (April 2016), published by the American Mathematical Society. © 2016 American Mathematical Society.
Peng, P., & Steele, J. (2016). Sequential Selection of a Monotone Subsequence from a Random Permutation. Proceedings of the American Mathematical Society, 144 4973-4982. http://dx.doi.org/10.1090/proc/13104
Date Posted: 25 October 2018
This document has been peer reviewed.