J Allikvere

Inversion monotonicity and asymptotic enumeration of 1324-avoiding permutations with few inversions

Let A(n,k) count the 1324-avoiding permutations of length n with k inversions, and let a(k) = sumj=0k p(j)p(k-j), where p is the partition function. We prove A(n,k) ≤ A(n+1,k) for 0 ≤ k ≤ floor(n2 / [20 log2(n+1)]), for every n ≥ 1. We also prove A(n,k)/a(k) = 1 + O(log log n / log n), uniformly for 0 ≤ k ≤ π2n2 / [12(...