An Upper Bound on the Number of $(132,213)$-Avoiding Cyclic Permutations

Brice Huang

doi:10.1016/j.disc.2019.02.011

An Upper Bound on the Number of $(132,213)$-Avoiding Cyclic Permutations

Combinatorics 2019-03-14 v2

Authors: Brice Huang

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Abstract

We show a $n^2 \cdot 2^{n/2}$ upper bound on the number of $(132,213)$ avoiding cyclic permutations. This is the first nontrivial upper bound on the number of such permutations. We also construct an algorithm to determine whether a $(132,213)$ avoiding permutation is cyclic that references only the permutation's layer lengths.

Keywords

cyclic permutations pattern avoidance permutation patterns upper bound layer lengths algorithm

Cite

@article{arxiv.1808.08462,
  title  = {An Upper Bound on the Number of $(132,213)$-Avoiding Cyclic Permutations},
  author = {Brice Huang},
  journal= {arXiv preprint arXiv:1808.08462},
  year   = {2019}
}

Comments

16 pages, 3 figures, 2 tables; typos corrected

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