Pattern avoidance in compositions and powers of permutations

Kassie Archer, Noel Bourne

A permutation $\ddot{I}€$ is said to avoid a chain $(\ddot{I}ƒ:\ddot{I}„)$ of patterns if $\ddot{I}€$ avoids $\ddot{I}ƒ$ and $\ddot{I}{€}^2$ avoids $\ddot{I}„.$ In this paper, we define a notion of pattern avoidance for composition…