In the paper, Levenshtein’s sequence reconstruction problem is considered in case where transmitted words are chosen from an e -error-correcting code, at most xmlns:xlink="http://www.w3.org/1999/xlink">t substitution errors occur each of xmlns:xlink="http://www.w3.org/1999/xlink">N chan...

Let Sn be the set of all permutations {1, 2, …, n} represented in cycle notation. Define an, m to number π ∈ such that length initial longest increasing sequence (ILIS) is at most m. For fixed m, we find exponential generating function for and give an asymptotic formula when n → ∞. Moreover, show expected value total ILIS cycles over e ∑j=1 1/j.