Monotone Subsequences in High-Dimensional Permutations
نویسندگان
چکیده
This paper is part of the ongoing effort to study high-dimensional permutations. We prove the analogue to the Erdős–Szekeres Theorem: For every k ≥ 1, every order-n k-dimensional permutation contains a monotone subsequence of length Ωk (√ n ) , and this is tight. On the other hand, and unlike the classical case, the longest monotone subsequence in a random kdimensional permutation of order n is asymptotically almost surely Θk (
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عنوان ژورنال:
- Combinatorics, Probability & Computing
دوره 27 شماره
صفحات -
تاریخ انتشار 2018