2 problems

Let $ath]σ\in\mathcal S_m$ be a non-overlapping pattern, meaning that two occurrences cannot overlap in more than one position. Let $\alpha_n(σ)$ be the number of permutations of l…

Let $ath]σ\in\mathcal S_m$ be a non-overlapping pattern, and let $\alpha_n(σ)$ be the number of permutations of length $n$ avoiding $ath]σ$. Nakamura's extremal conjecture. For eve…