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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.

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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

R2 v1 2026-06-21T22:03:23.930Z