On the Best Upper Bound for Permutations Avoiding A Pattern of a Given Length
Combinatorics
2012-09-12 v1
Abstract
Numerical evidence suggests that certain permutation patterns of length k are easier to avoid than any other patterns of that same length. We prove that these patterns are avoided by no more than (2.25k^2)^n permutations of length n. In light of this, we conjecture that no pattern of length k is avoided by more than that many permutations of length n.
Cite
@article{arxiv.1209.2404,
title = {On the Best Upper Bound for Permutations Avoiding A Pattern of a Given Length},
author = {Miklos Bona},
journal= {arXiv preprint arXiv:1209.2404},
year = {2012}
}
Comments
12 pages