3 problems

Let $S_n$ be the set of separable permutations of length $n$, and for $\pi\in S_n$ let $\operatorname{lmax}(\pi)$, $\operatorname{rmax}(\pi)$, $\operatorname{lmin}(\pi)$, and…

Discrete–continuum exponent conjecture. With probability tending to $1$ as $n\to\infty$,

The extremal Möbius-value conjecture. For every separable permutation $\pi$ of length $n\ge3$, the maximum value of $\mu(\sigma,\pi)$ is attained by a permutation of this form, wit…