Permutations that strongly avoid 132

Abstract

A permutation $\ddot{I}€$ strongly avoids the pattern $\ddot{I}„$ if both $\ddot{I}€$ and $\ddot{I}{€}^2$ avoid $\ddot{I}„$. In this paper, we enumerate permutations of size $n$ that strongly avoid the pattern 132. This enumeration allows us to prove a conjecture that the growth rate of such permutations is 2.