Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Monotone Subsequences in High-Dimensional Permutations   This paper is part of the ongoing effort to study high-dimensional
permutations. We prove the analogue to the Erd\H{o}s-Szekeres theorem: For
every $k\ge1$, every order-$n$ $k$-dimensional permutation contains a monotone
subsequence of length $\Omega_{k}\left(\sqrt{n}\right)$, 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 $\Theta_{k}\left(n^{\frac{k}{k+1}}\right)$.

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The categories of this paper are: eess
29
The categories of this paper are: funct-an
22
The categories of this paper are: chao-dyn
37
The categories of this paper are: supr-con
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The categories of this paper are: alg-geom
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The categories of this paper are: nucl-th
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The categories of this paper are: hep-ex
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The categories of this paper are: dg-ga
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The categories of this paper are: hep-th
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The categories of this paper are: q-alg
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The categories of this paper are: nlin
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The categories of this paper are: chem-ph
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The categories of this paper are: solv-int
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The categories of this paper are: patt-sol
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The categories of this paper are: ao-sci
1
The categories of this paper are: cs