3 problems

Interval-heapability scaling conjecture. For every k\boldsymbol{ there exists $c_k>0$ such that

Let $k\geq 2$, and let $W_n$ be a set of $n$ random intervals. Write $E[k\operatorname{-wd}(W_n)]$ for the expected $k$-width of $W_n$. Random-interval set scaling conjecture. Ther…

Let $k\geq 2$, and let $R_n$ be a sequence of $n$ random intervals. Write $E[k\operatorname{-wd}(R_n)]$ for the expected $k$-width of $R_n$. Random-interval sequence scaling conjec…