Permutations avoiding 312 and another pattern, Chebyshev polynomials and longest increasing subsequences
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.
- Publication:
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arXiv e-prints
- Pub Date:
- August 2018
- DOI:
- 10.48550/arXiv.1808.05430
- arXiv:
- arXiv:1808.05430
- Bibcode:
- 2018arXiv180805430M
- Keywords:
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- Mathematics - Combinatorics
- E-Print:
- 14 pages, 1 table, Lemma 2.1 added, some additions and minor corrections made