The Prolific Proportion of Permutations
Cheyne Homberger, Peter M. Winkler · arXiv (Cornell University) · 2017
A permutation is $d$-prolific if every choice of $d$ entries to delete results in a different pattern. In this note, we prove that the proportion of $d$-prolific permutations in the set of all permutations is asymptotically equal to $e^{-d^2 - d}$.