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A probabilistic approach to the asymptotics of the length of the longest alternating subsequence
The electronic journal of combinatorics, Tome 17 (2010)
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Let $LA_{n}(\tau)$ be the length of the longest alternating subsequence of a uniform random permutation $\tau\in\left[ n\right] $. Classical probabilistic arguments are used to rederive 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 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.
DOI : 10.37236/440
Classification : 60C05, 60F05, 60G15, 60G17, 05A16
Mots-clés : longest alternating subsequence, random permutations, random words, \(m\)-dependence, central limit theorem, law of the iterated logarithm 
@article{10_37236_440,
     author = {Christian Houdr\'e and Ricardo Restrepo},
     title = {A probabilistic approach to the asymptotics of the length of the longest alternating subsequence},
     journal = {The electronic journal of combinatorics},
     year = {2010},
     volume = {17},
     doi = {10.37236/440},
     zbl = {1203.60013},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/440/}
}
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Christian Houdré; Ricardo Restrepo. A probabilistic approach to the asymptotics of the length of the longest alternating subsequence. The electronic journal of combinatorics, Tome 17 (2010). doi: 10.37236/440

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