TY - JOUR
T1 - Monotone Subsequences in High-Dimensional Permutations
AU - Linial, Nathan
AU - Simkin, Michael
N1 - Publisher Copyright:
Copyright © 2017 Cambridge University Press.
PY - 2018/1/1
Y1 - 2018/1/1
N2 - 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)).
AB - 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)).
UR - http://www.scopus.com/inward/record.url?scp=85032195542&partnerID=8YFLogxK
U2 - 10.1017/S0963548317000517
DO - 10.1017/S0963548317000517
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AN - SCOPUS:85032195542
SN - 0963-5483
VL - 27
SP - 69
EP - 83
JO - Combinatorics Probability and Computing
JF - Combinatorics Probability and Computing
IS - 1
ER -