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For a fixed permutation τ, let S N (τ) be the set of permutations on N elements that avoid the pattern τ. Madras and Liu (2010) conjectured that lim N→∞ |S N+1 (τ)| |S N (τ)| exists; if it does, it must equal the Stanley–Wilf limit. We prove the conjecture for every permutation τ of length 5 or less, as well as for some longer cases (including 704 of the… (More)

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