On two conjectures about pattern avoidance of cyclic permutations

Junyao Pan

Let $\ddot{I}€$ be a cyclic permutation that can be expressed in its one-line form as $\ddot{I}€=\ddot{I}{€}_1\ddot{I}{€}_2\cdot \cdot \cdot \ddot{I}{€}_n$ and in its standard cycle form as $\ddot{I}€=(c_1,c_2,...,c_n)$ where…