On the Best Upper Bound for Permutations Avoiding A Pattern of a Given Length
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 (2.25k2)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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