Monotone Subsequences in High-Dimensional Permutations

Nathan Linial, Michael Simkin

Research output: Contribution to journalArticlepeer-review

5 Scopus citations


This paper is part of the ongoing effort to study high-dimensional permutations. We prove the analogue to the Erdos-Szekeres theorem: For every k ≥ 1, every order-n k-dimensional permutation contains a monotone subsequence of length Ω k , and this is tight. On the other hand, and unlike the classical case, the longest monotone subsequence in a random k-dimensional permutation of order n is asymptotically almost surely Θ k(n k/(k+1)).

Original languageAmerican English
Pages (from-to)69-83
Number of pages15
JournalCombinatorics Probability and Computing
Issue number1
StatePublished - 1 Jan 2018

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Copyright © 2017 Cambridge University Press.


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