\b[Yes, for arbitrary signed weights.] A <hyperedge> meets both $S$ and $V\setminus S$ exactly when it meets both $V\setminus S$ and $S$. Therefore $\delta(S)=\delta(V\setminus S)$, and their weighted sums agree. The <hypergraph cut function> is a <symmetric set function> regardless of the signs of its weights.

Solution

Past exam of the computer science course of the University of Oxford / 2023 / Combinatorial optimisation / 1 / d / i / Solution

 Solution (source code)