On two conjectures about pattern avoidance of cyclic permutations

Junyao Pan

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