Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A probabilistic approach to the asymptotics of the length of the longest
  alternating subsequence   Let $LA_{n}(\tau)$ be the length of the longest alternating subsequence of a
uniform random permutation $\tau\in[n]$. Classical probabilistic arguments are
used to rederive the asymptotic mean, variance and limiting law of
$LA_{n}(\tau)$. Our methodology is robust enough to tackle similar problems for
finite alphabet random words or even Markovian sequences in which case our
results are mainly original. A sketch of how some cases of pattern restricted
permutations can also be tackled with probabilistic methods is finally
presented.

24
The categories of this paper are: dg-ga
35
The categories of this paper are: mtrl-th
27
The categories of this paper are: comp-gas
16
The categories of this paper are: stat
31
The categories of this paper are: ao-sci
33
The categories of this paper are: plasm-ph
15
The categories of this paper are: nucl-ex
34
The categories of this paper are: chem-ph
25
The categories of this paper are: patt-sol
37
The categories of this paper are: supr-con
18
The categories of this paper are: econ
6
The categories of this paper are: astro-ph
13
The categories of this paper are: quant-ph
22
The categories of this paper are: chao-dyn
9
The categories of this paper are: nlin
14
The categories of this paper are: math-ph