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

Brice Huang

doi:10.1016/j.disc.2019.02.011

paper

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

arXiv:1808.08462 · doi:10.1016/j.disc.2019.02.011

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.

16 pages, 3 figures, 2 tables; typos corrected

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

Abstract

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