# Covering a symmetric crossing supermodular function with hyperedges of prescribed size

Given a symmetric crossing supermodular function $p:2^V\to \mathbb{R}$ and positive integers $n_1,n_2,\dots,n_k$, does there exist a hypergraph H=(V,E) covering p and having exactly k hyperedges of sizes $n_1,n_2,\dots,n_k$?

## Remarks

If the sizes are all equal then the problem was solved by Tamás Király [1].

## References

1. T. Király Covering symmetric supermodular functions by uniform hypergraphs DOI Link