1324-avoiding permutations revisited

2017/09/05 by Conway, Andrew R., Guttmann, Anthony J., Zinn-Justin, Paul · 1 citation
#Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.1709.01248

Abstract

We give an improved algorithm for counting the number of 1324-avoiding permutations, resulting in 14 further terms of the generating function, which is now known for all patterns of length ≤ 50. We re-analyse the generating function and find additional evidence for our earlier conclusion that unlike other classical length-4 pattern-avoiding permutations, the generating function does not have a simple power-law singularity, but rather, the number of 1324-avoiding permutations of length n behaves as B⋅ μⁿ ⋅ μ₁^√(n) ⋅ n^g. We estimate μ=11.600 ± 0.003, μ₁ = 0.0400 ± 0.0005, g = -1.1 ± 0.1 while the estimate of B depends sensitively on the precise value of μ, μ₁ and g. This reanalysis provides substantially more compelling arguments for the presence of the stretched exponential term μ₁^√(n).

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