3 problems

Influence submodularity conjecture. The function $\sigma$ is submodular.

Mixed-hypergraph orientation conjecture. There exists an orientation $\overrightarrow{\mathcal{E}}$ of $\mathcal{E}$ such that

Let $\mathcal X$ be a family of subsets of a finite set $E$, and let $\operatorname{val}_{\mathcal X}$ be the set function defined from proper $\mathcal X$-sequences. Suppose there…