%0 Journal Article
%T A probabilistic approach to the asymptotics of the length of the longest alternating subsequence
%A Christian Houdr¨¦
%A Ricardo Restrepo
%J Mathematics
%D 2010
%I arXiv
%X 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.
%U http://arxiv.org/abs/1005.1893v2