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arXiv · 1808.05430

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

Toufik Mansour·Gökhan Yıldırım
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Abstract

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.

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Toufik Mansour, Gökhan Yıldırım. 2020-01-24. Permutations avoiding 312 and another pattern, Chebyshev polynomials and longest increasing subsequences. https://doi.org/10.1016/j.aam.2020.102002

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