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

Toufik Mansour; Gökhan Yıldırım

doi:10.1016/j.aam.2020.102002

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

Combinatorics 2020-01-28 v2

Authors: 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 $\tau$ 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 $\tau$ is monotone increasing or decreasing, or any pattern of length four.

Keywords

pattern avoidance in permutations permutations integer sequences and recurrences

Cite

@article{arxiv.1808.05430,
  title  = {Permutations avoiding 312 and another pattern, Chebyshev polynomials and longest increasing subsequences},
  author = {Toufik Mansour and Gökhan Yıldırım},
  journal= {arXiv preprint arXiv:1808.05430},
  year   = {2020}
}

Comments

14 pages, 1 table, Lemma 2.1 added, some additions and minor corrections made

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

Abstract

Keywords

Cite

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