Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the number of monotone sequences   One of the most classical results in Ramsey theory is the theorem of
Erd\H{o}s and Szekeres from 1935, which says that every sequence of more than
$k^2$ numbers contains a monotone subsequence of length $k+1$. We address the
following natural question motivated by this result: Given integers $k$ and $n$
with $n \geq k^2+1$, how many monotone subsequences of length $k+1$ must every
sequence of $n$ numbers contain? We answer this question precisely for all
sufficiently large $k$ and $n \leq k^2 + c k^{3/2} / \log k$, where $c$ is some
absolute positive constant.

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The categories of this paper are: eess
13
The categories of this paper are: quant-ph
6
The categories of this paper are: astro-ph
18
The categories of this paper are: econ
1
The categories of this paper are: cs
36
The categories of this paper are: cmp-lg
32
The categories of this paper are: atom-ph
31
The categories of this paper are: ao-sci
37
The categories of this paper are: supr-con
33
The categories of this paper are: plasm-ph
16
The categories of this paper are: stat
7
The categories of this paper are: hep-th
34
The categories of this paper are: chem-ph
27
The categories of this paper are: comp-gas
10
The categories of this paper are: q-bio
9
The categories of this paper are: nlin