... 2n−1k=1k Covf, T(k)f, (14) the electronic journa l of combinatorics 17 (2010), #R168 11A probabilistic approach to the asymptotics of the length of the longest alternating subsequenceChristi ... the lines of the previous section, re-lating the counting of maxima to the length of the longest alternating subsequence andthen, through mixing and ergodicity, obtain results on the asymptotic ... sm. the electronic journa l of combinatorics 17 (2010), #R168 10Theorem 4.2 Let LAn(x0, . . . , xn) be the length of the longest alternating subsequence of the first n + 1 elements of the...