Crucial and bicrucial permutations with respect to arithmetic monotone patterns

Sergey Avgustinovich, Sergey Kitaev, Alexandr Valyuzhenich

A pattern $\tau$ is a permutation, and an arithmetic occurrence of $\tau$ in (another) permutation $\pi ={\pi }_1{\pi }_2...{\pi }_n$ is a subsequence ${\pi }_{i_1}{\pi }_{i_2}...{\pi }_{i_m}$ of $\pi$ that is order isomo…