We 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.
Bibliographical notePublisher Copyright:
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- Chebyshev polynomials
- Generating functions
- Longest increasing subsequence problem
- Pattern-avoiding permutations
ASJC Scopus subject areas
- Applied Mathematics