1324-avoiding permutations revisited

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 lengths ≤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⋅μ1n⋅ng. 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 argu..