A note on the length of the longest alternating subsequence

Details A note on the length of the longest alternating subsequence A note on the length of the longest alternating subsequence

2010-05-11

arxiv.org/abs/1005.1893v1

Mathematics

Probability

Scientific paper

Let $LA_{n}(\tau)$ be the length of the longest alternating subsequence of a
random permutation $\tau\in\left[ n\right] $. Classical probabilistic arguments
are provided to derive the asymptotic mean, variance and limiting law of
$LA_{n}\left( \tau\right) $. Our methodology is robust enough to tackle similar
problems for finite alphabet random words or even Markovian sequences.

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