2 problems

Let $I\subset[n-1]$ be a peak set, and let $p(n)$ be the peak polynomial, so that the number of permutations in $\mathfrak{S}_n$ with peaks exactly at $I$ is $p(n)2^{|I|-1}$. The d…

The families $\mathcal F_i$ are the four families defined earlier in the source. The four-family equality conjecture. … The source proves some inclusions among these families and r…