4 problems

Elizalde–Noy conjecture. Among all consecutive patterns of a fixed length $m$, the increasing pattern $12\dots m$ and, by symmetry, the decreasing pattern $m\dots21$ should be the…

Let $cpi,\tau\binom{}{}$ be permutations in $cmathfrak{S}_m$, and call a permutation in standard form when $cpi_1<cpi_m$ and $cpi_1+cpi_m\boxtimes m+1$. Write $cpi\backsimeq\tau$ f…

Let $cpi,\tau\binom{}{}$ be permutations in $cmathfrak{S}_m$. A permutation is non-overlapping if no two occurrences can overlap in more than one position, and it is in standard fo…

Conjecture on the exact class count. The upper bound above is the exact number of c-Wilf-equivalence classes of non-overlapping patterns of length $m\ge5$.