Permutations avoiding 312 and another pattern, Chebyshev polynomials and longest increasing subsequences

Mansour, T.Yıldırım, Gökhan2021-02-112021-02-1120200196-8858http://hdl.handle.net/11693/55083We study the longest increasing subsequence problem for random permutations avoiding the pattern 312 and another pattern τ under the uniform probability distribution. We determine the exact and asymptotic formulas for the average length of the longest increasing subsequences for such permutation classes specifically when the pattern τ is monotone increasing or decreasing, or any pattern of length four.EnglishLongest increasing subsequence problemPattern-avoiding permutationsChebyshev polynomialsGenerating functionsPermutations avoiding 312 and another pattern, Chebyshev polynomials and longest increasing subsequencesArticle10.1016/j.aam.2020.102002